Whilst you can use laptops on your lap, it's ONLY if they are on a hard, flat surface such as a tray. Most laptops suck air up from underneath to cool the insides, blowing hot exhaust out of a side/rear port. Any surface which is not smooth and hard (i.e. human laps, rugs, cushions, bedding, carpet, towels, coats) will almost certainly block the intake grille causing the laptop to overheat and eventually shut down (or burn out, if it's a really nasty one). If it's too hot to touch, it's already killing itself - electronics hate heat, especially batteries and hard-drives. Regularly clean the intake of fluff, hair & clogged up dust, or it will die prematurely.
If it is the battery that is very hot, then DON'T USE IT - take it back to the dealer! As has been mentioned, there have been many cases of battery fires (and the occasional injury) involving bad batteries and/or their charging circuitry. Lithium batteries are not to be messed with, they can 'vent with flaming matter' (explode) if badly abused.
You should be able to get the whole thing replaced under warranty. Mention 'battery fire injury lawsuit' if they give you any nonsense.