A hot plug can cause a fire.
A plug can get somewhat warm such as with a space heater but it should not be very hot and only warm to the touch.
If the plug is hot or the outlet is hot then the appliances or plug should be unplugged to prevent a fire.
It's not normal for plugs or outlets to get hot although they can get a bit warm.
When a plug or outlet is getting hot it's likely because of a loose connection or a bad outlet.
The outlet may not be holding the plug in tight enough which leads to resistance in the circuit which then heats up the outlet and plug.
Also if you smell a burning smell or the outlet is actually hot or you smell a fishy smell then you should shut the breaker off those those outlets that are hot.
Then contact an electrician or if you can do the work yourself get a new plug and fix the issue.
Electrical fires can happen at anytime and can occur while you're asleep as well.