Is it normal for iphone x to be heated up when serving as hot spot?

The general answer is that it is normal; cellular data is the heaviest user of energy on any phone. So you have the heat lost in the less than 100% efficient RF radio (2nd law of thermodynamics) plus the heat lost in the less than 100% efficient battery (2nd law again). The actual energy required depends on signal strength; the RF transmitter uses 10 times as much energy if the connection is one bar over a five bar connection. You normally don't notice this using cellular data or voice, because it is for relatively short periods of time. But a hotspot connection keeps a continuous connection. And it also uses Wi-Fi continuously, adding 30 mw to the already heavy cellular load of 50 mw to 500 mw (depending on signal strength).

If you happen to be charging at the same time then that also adds to the heat generation (2nd law yet again).

Obviously I can't judge that "heat" remotely, but I would consider it a normal behavior, using hotspot.

To feel more comfortable, since your iPX is still under warranty, I would contact your most convenient Apple Store or Authorized Service Provider and let them check your device. They will give you all the available explanations / options:

Apple - Find Locations - Location Selector

Regards

Giulio

Yes it is going to heat up. The better your cell connection (more bars ) the less heat it will generate.

I’d think it would maybe get a little warm. As it is kinda working in background.