Baking Double Pans of Muffins
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.