Thank you very much for your willingness to help me out.
The bit I'm using is a straight bit, 1/4" shank and 1/4" diameter, taking 1/8" deep cut every time, for 4 inches long at a time.
The battery is not getting hot at all, it remains cool, no change is happening to the battery.
By getting overheating I mean that I'm not able to catch the collet with my fingers, only with a cloth or something, and I can't grab the router's body for more than 5 seconds.
I wanted to inform that today I returned the trimmer to the seller, so he can fix it or replace it for me.
I appreciate your time and effort.