Do you need to adjust baking time or temperature when baking more than one pan of muffins at the same time in a single oven?
Quick answer: No adjustments mandatory.
To explain: You will need to adjust baking times when you change the "lump" of batter to be baked. Examples: Mini or Jumbo muffins instead of regular ones. Coffe cake in a loaf or round pan, bread or rolls. Rule of thumb: thicker cake, more time. That's why you use a wooden skewer to test for doneness. As far as the temperature is concerned, usually you should be fine with the given value of your original recipe. If in doubt, rather go down for larger cakes (to prevent burning), but go up for bread (but lower again after 15 minutes or so.)
So for your question:
- Make sure you preheat your oven properly, maybe even 10 degrees higher (but turn back once the muffins are in the oven), because two tins will lower oven temperature more than one tin.
- Perhaps rotate / switch places of your tins halfways, if your reipe is ok with opening the oven door, most muffins are.
As long as the source is reputable, the baking instructions will always provide enough information to prevent your ever having to worry over this question. So the answer is definitely no. (It's not the only reason the answer is no, but it goes to the implied fact that you're following a set of instructions.) And since it may help to look at just how those instructions manage to exclude this as a problem, I will add just these few more remarks.
If the baking instructions say to place the pan on the center rack, especially if they say "in the center of the oven", it typically means also to say (to have understood) that each batch should be baked separately. But this added instruction is not to prevent one's needing to adjust baking times or temperatures. Instead, it's to prevent a less than ideal outcome in terms of quality.
To explain, for some baked goods it is important that the heat flow evenly around the pan and not be absorbed or reflected by another pan (which happens when pans are stacked on separate racks). For some baked goods it is important to avoid getting the pan too close to any particular wall of the oven (which happens when pans are placed side by side). For some baked goods both of these issues can even come into play at the same time, that is, in a bad way. There may be types of muffins for which such matters are known to have bearing.
By and large however, for reasons most would find self-evident, the baking instructions aren't going to go into all these whys and wherefores. They'll just say to place the pan on the center rack of the oven. If they don't say that, usually it's okay to double up, triple up, or even more if your oven will hold it. But this again assumes the source of your instructions to be credible.
On a separate but entirely relevant note, it is good to know that the temperature of a preheated oven remains virtually unchanged (or, more specifically, goes largely unaffected) by the introduction of multiple pans, therefore requiring no increase in the specified temperature or the recommended baking time. The reason for this is that the amount of mass in metal which lines an oven (plus the racks themselves) greatly exceeds the amount of mass in metal being introduced to the system in the form of pans. I suppose a good analogy would be spreading a few spoons about a hot griddle. Though the temperature of the spoons would rise almost instantly, and would soon reach nearly that of the griddle, the temperature of the griddle wouldn't have dropped by even one degree at/from the time the spoons were introduced.