The resources for this topic are terrible. The best I have come up with is reasoning from first principles. That reasoning suggests the probable temperature at which spores are destroyed is somewhere between 113.3C and 116.4C, but without a proper microbiology experiment it's hard to say with much certainty whether that's correct.
Problems with Existing Resources
None of the resources on this topic that I have reviewed provide a credible answer to the question of what exposure time, temperature, and pH is required to destroy C. botulinum. At best they provide confusing and ambiguous statements none of which seem to be substantiated by experimental evidence.
I have not performed an exhaustive review of academic journals for this topic. Hopefully, an experiment from a specialist on this topic will surface, but given the dearth of references to such materials I encountered, I'm not optimistic.
Conflation of Process versus Spore Time and Temperature
All of the resources I have reviewed on this topic are imprecise in a critical way: The stated process times and temperatures required to destroy the spores are not distinguished from the time the spore itself must be held at temperature to destroy it. For example, the USDA's "Home Canning Guide 1 - Principles" states the following:
At temperatures of 240° to 250°F, the time needed to destroy bacteria in low-acid canned food ranges from 20 to 100 minutes. The exact time depends on the kind of food being canned, the way it is packed into jars, and the size of jars.
The only interpretation of this statement that makes sense to me is that the phrase "At temperatures of 240° to 250°F" here refers the temperature the spores must eventually reach while the "time needed to destroy bacteria" refers to process time. That is it might take exposing a can to that temperature "20 to 100 minutes" such that all of its contents reach a high enough temperature for long enough to destroy the spores. In other words, the critical targets for spore and process are ambiguously discussed within a single sentence. This conflation is characteristic of all documents on this topic that I have reviewed.
It's difficult for me to understand how the authors and editors of these publications decided that introducing this kind confusion into a topic of such import is helpful.
Absence of Scientific Data
I am further skeptical of the veracity of the resources I have reviewed published on this topic because none of them include references to any scientific literature measuring the relationship between exposure time, temperature, pH, and survival rates of C. botulinum spores. I have searched for the same and come up empty handed. It seems that all of the recommendations I have found for destroying C. botulinum are not based on scientific evidence.
Analysis from First Principles and Customary Practices
Absent the results of some sort of a microbiology experiment performed by a competent empiricist, the best I can hope for is to infer what temperatures spores must have customarily reached in successful home canning environments over the past decades. To make this inference, I'm relying on the well-established thermodynamic principles forming the basis of the pressure canning process, and some assumptions about what must have been happening in those millions of cans of food that must have been successfully preserved without causing botulism.
Newton's Law of Heating
Pressure canning is a thermodynamic system where the cans are immersed in a heat reservoir by way of establishing a water/steam vapor-liquid equilibrium at a particular stable temperature. The temperature of any point on the inside of the can is described by Newton's law of heating and cooling:
where t is time since the the water/steam reached , T is the temperature of the point, is the temperature of the water/steam in equilibrium, and τ is the time constant that is characteristic of that particular point.
By way of a qualitative understanding of the heat equation applied to that thermodynamic system, the lowest temperature point inside the can while heating will be at the thermodynamic center of the can. The thermodynamic center corresponds to the mechanical centroid of the can assuming the can and contents have homogeneous thermodynamic properties. As best I can tell, the process times and temperatures commonly recommended to destroy C. botulinum correspond to the time expected for this coolest point to reach and exceed some temperature long enough to destroy the spores.
I have measured the time constant for my own bolognese sauce on my stovetop in a one-liter jar in steam/water equilibrium at one atmosphere with the following results:
Note that R² has four nines which, I think, qualifies this as another example of Wigner's observation. For this particular jar of bolognese τ is 41 minutes.
The important property of Newton's law for pressure canning is that the coldest point in the can approaches but never reaches the temperature of the steam. Accordingly, the temperature of the spores inside the can are always somewhat less than the temperature of the steam/water equilibrium.
Customary Process Pressures and Temperatures
Where I live the most common manufacturer of pressure canners I encounter is National Presto Industries. I have heard many accounts from at least two generations my senior of regularly canning meat, seafood, fruits, and vegetables using Presto pressure cookers. In my region of Canada, at least, it seems like it is customary to simply strictly follow the Presto instructions for the food product when canning. None of the canners I have spoken with mentioned food-borne illnesses where they suspected the cause was canning. I take this to mean that whatever the process that has been prescribed by Presto is sufficient to destroy C. botulinum spores.
I have a paper manual of a Presto 418 from what I think was the 1970s. I also have the manual from amazon's #1 best seller pressure canner, the Presto 01781.
The former prescribes the following for all meats:
PROCESSING TIME TABLE MEATS
Amount of Pressure Pounds: 10
Quarts Minutes: 90
The latter prescribes the following for Spaghetti Sauce:
Spaghetti Sauce with Meat
Pressure canning: Process at 11 pounds pressure...quarts 70 minutes.
These gauge pressure values of 10 and 11 psig correspond to 115.2C (239F) and 116.4C (241F), respectively.
While I have not come across any data measuring the prevalence of meat canning using Presto pressure canners, I have encountered some examples of that myself. With respect to prevalence of botulism in this region, Health Canada states the following:
While outbreaks of food-borne illnesses in Canada are relatively common, botulism outbreaks are quite rare. In recent years, about two cases per year have been reported in Canada.
In general, the time constant for Newton's Law differs for of each combination of food and canning jar. We could make the reasonable but unproven assumption that the time constant of the Spaghetti sauce process from the Presto 01781 manual is the same 41 minutes as the measured time constant of my bolognese. Assuming a starting temperature of 100C, a water/steam equilibrium temperature of 116.4C, and the 70 minute process time prescribed by the Presto manual, the minimum temperature of my bolognese would reach 113.3C at the 70 minute mark. By dint of the heat equation, that minimum temperature would have continued to approach the water/steam equilibrium temperature for some time after the heat was removed from the canner.
Based on this, I think it can be concluded that users of Presto canners who strictly follow the instructions have been successfully canning meats where the maximum temperature reached by the meat was less than 116.4C (241F). I think it can also be concluded that those same users were probably achieving a minimum temperature of at least 113.3C (236F). This suggests a range of between 113.3C and 116.4C wherein the minimum temperature at which C. botulinum spores are likely to be destroyed would lie.
This is not at all a conclusion that I would consider to be beyond reproach. But at least what underlies this conclusion is reasoning from first principles which seems to be an epistemic improvement over the other resources on this topic that I have found. You'll have to decide for yourself whether this line of reasoning is good enough to rely on for your health.