Say I want to cook fresh pasta and I don't have access to a stove or hotplate. I can heat water with an immersion circulator. I can get close, but can't achieve a boil. What is the lowest temperature needed to cook fresh (water and/or egg based...but not dried) pasta? While I provide the circulator as an example, this is less of a modernist technique question and more of a science of cooking pasta question.
Cooking pasta at a full rolling boil (100°C at sea level or less at higher altitudes) is just conventional, it is not the boiling the cooks pasta but the temperature:
pasta cooking is influenced by three factors: water penetration inside the pasta, gelatinization of the starch (it normally occurs at a temperature between 60°C and 70°C for wheat starch) and the denaturation and consequent coagulation of gluten (at 70°C-80°C). A temperature above 80°C for a certain time (slightly longer than what you'd need at 100°C to compensate for the slower penetration of water into the pasta) should guarantee a perfectly cooked pasta.
This is the same for dried pasta and for fresh pasta; fresh will cook in less time, and you should probably taste it during the cooking process to find the right texture.
The rolling boil helps to keep the pasta well separated and to avoid sticking, but a water circulator would probably take care of that too
Even if it loses its boil, the pasta will still continue to cook so long as it's kept above 180°F/80°C or so.