Does everything scale linearly in cooking?

Ingredients mostly do, but not always. Salt and baking powder should be scaled to 75-80% when doubling. Spices can be scaled to 1.5× when doubling. Cooking time may increase for larger volumes. And yeast in bread can stay the same up to about 3× the recipe.

Should I adjust baking temperature when scaling?

Generally no. Temperature stays the same. Time increases slightly for larger volumes. A doubled cake recipe in a larger pan may need 5-10 extra minutes. Use a toothpick or thermometer to check doneness.