Adjusting Cooking For Smaller Portions
It is difficult to offer a general answer applicable to all recipes and all cooking methods.

In almost all situation, there is no need to change temperature (I cannot think of any exceptions off the top of my head, but I am sure others will think of a few).

The most obvious effect portion size has on cooking time is the time needed to take the food from starting temperatures (say from freezer or fridge or room temperature) to cooking temperatures. Once the food is reaches cooking temperature and if there is a need to cook it further by holding it at that temperature for a certain amount of time (for example a casserole has holding time requirement, but a piece of steak does not), this time should not change regardless of portion size. 

For the same stove or oven and at the same setting, half the amount of food by weight will take half the energy to raise it to cooking temperature, a linear relationship. However, the transfer of heat into the food is strongly influenced by the shape of the food, surface area and thickness. This affects the time it takes to raise the food's temperature. This is where "it depends" matters. If you are comparing a small chicken to a large chicken, then size difference is usually accompanied by change in surface area and thickness. A 1kg chicken will take more than twice the time than a 0.5kg chicken. However, if you are cooking one piece of chicken breast instead of two pieces of the same, the heating time will be halved. 

If you are making two trays of pasta bake, then cooking just one of the two trays will take half the heating time and unchanged holding time. However, if you are going from one big tray to one small tray with half the quantity, the change in geometry (thickness and surface area) will mean that heating time change is no longer a straight forward linear decrease.

In practice, doing a heat calculation will only give you a very rough idea so that you know where to aim, but you will need to test it and get an empirical relationship.

Edit: There is one more caveat. Imagine frying a piece of chicken breast in an open pan. You will likely find that adding another piece (or more) does not change cooking time noticeably. They probably all cook to the same doneness in the same duration. That happens because with a single piece, especially in a large pan, there is considerable "wasted heat". Your stove is likely putting out far more heat than there is food too cook most of the time and you end up heating up of kitchen air.