If you have to run it with the choke after it has warmed up, you need to disassemble the carb for cleaning.
A sheared flywheel key (advanced timing) will often cause a red hot muffler. This happens when the mower blade hits a stump, rock, etc.
Considering that it is probably a motorized one. Yes. Anything that has an engine can more then likely get hot.
If its a new mower take it back to where you bought for warranty If you mess with it you will forfeit your warranty.
Bypass the switch with a jumper & see if you can bump it with a hot wire.
In cooler temperatures it's ok, but in hot weather run a thicker oil.
In hot weather it would (or should) not be a problem. 30wt and 10W30 are generally the rule.
did you check and make sure you have plenty of oil. or maybe your lawn mower just needs a break.
Just make sure the engine is not running and pour in the fuel. If the engine is hot let it cool before refueling.
You feel less hot and thirsty.
Sounds like a ignion coil.
let it cool down. change oil adn things then try again! also check blades could be faulty auto choke if equipped, when hot check for spark coil could be going bad
There may be a number of issues with the lawn mower. The motor may need oil or gas. The intake filter may be too dirty, clean it up then put it back in when it is dry. The blades might not be able to spin around, maybe something is obstructing them, causing the machine to not turn over the engine / motor.