I think your definition of overheating could well be a normal situation as the cpu will go 100% on any computer when browsing, the other factor could be the battery losing the ability to hold a charge and you can only check that by replacing the battery.

Gaming will for sure make the cpu high in usage and could very well be why your device is getting hot but i still say you need to check the battery first and take into consideration what your actually doing on it to overheat, so far you have picked the 2 most common high cpu usage as in gaming and browsing.