Does increasing AWG increase temperature?
Increasing the AWG number of your wire increases resistance. Higher AWG Has smaller area

$$R = (\rho *L)/A $$

Therefore, higher AWG has more resistance. And more resistance with the same current means more heat is dissipated.

The link below shows different diameters of AWG wire:
https://www.tedpella.com/company_html/wire-gauge-vs-dia.htm

Here is also a link for the resistance per foot of different AWG wire:

http://www.picwire.com/technical/wire.php