Wouldn't think overheat the phone like crazy?
Linux is more lightweight than Windows. Linux use less system resources like RAM, CPU, and video resources than Windows.
Debian Linux is very lightweight where it run on a PC which has a 1 GHz CPU , and 128MB of RAM according to its Minimum System Requirments listed on
https://en.wikipedia.org/wiki/Debian#Hardware_requirements
If you run Debian in the command line user interface, you just need 64MB of RAM.
Debian is even more lightweight than Google Android, Apple iOS and other mobile operating systems which are becoming more RAM and CPU intensive.
But, Linux compatible programs like Libreoffice, Firefox, Chromium, and Gimp may make the smartphone overheat more if the programs need a lot of RAM, and a faster CPU to run smoothly.