Depends how hot. From my experience, most of the time after extended use, they're gonna get hot, but I mean if it's like burning your hand or hot enough to melt something, I'd be concerned.
I'm with thedudeman. If it's hot after a hour or so, it's nothing to be worried about. Also, make sure you don't over-charge your battery. It can do more bad than good.
Also, maybe try and get a labtop cooler to put underneath your labtop.
It is uncomfortably hot when I touch it. My guest is about 40 ºC / 104 ºF . But, it is not burning hot. It kind of feels like a hair dryer's heat when I'm charging the battery, or doing CPU intensive stuff.
I think I solved the heat problem by using an electric fan to blow air on to the laptop power adapter.
Put it on carpet = No
Put it on while your laptop is on = No, unless you have no/low battery.
Use a fan to cool it = Not really as your laptop will be blowing out hot air and if your in a enclosed room that fan is just going to blow that hot air back on your laptop adapter.
Use a laptop = No, desktops OWN 😀!!.