How warm does the Apple Watch get while charging

Warm enough that it mightn't be comfortable to wear until it's cooled off a little.

I often charge my Watch while streaming music over LTE in a 30c/86f degree warehouse. If I don't keep it in front of a fan it disables LTE after a while to let things cool down - Hahaha! All normal though.

Is it the Apple charger or a 3rd party charger?

Inductive charging does generate heat in the charger and that of course could be transferred to the Apple Watch via physical contact.

My Apple Watch Charger and the 3rd party night stand charger I got do not heat up my Apple Watch very much. It is warm, but I would say not more than a few degrees warmer than my skin surface temperature, so not very warm at all.

If yours is to hot to put on your wrist comfortably, it is too hot. If Apple charger, then you should be talking to Apple about the watch being to hot. If it is a 3rd party charger, then try the Apple Charger and by the process of elimination try to narrow it down to the component that it generating the heat.

It will get warm, but my warm and your hot may be the same thing, as I'm not sure what constitutes hot to you vs what I think is warm.

If it is too hot to touch, that is not normal.