I believe that is not a law that you are talking about, but it is a guarantee paper which you get by the shop when you buy some thing in it..It can be valid for two, three years or more, and when product that you bought got damaged (in that time period and not by you) you can go there and ask for a new one (in your case laptop)..So yeah, if you got heat problems, you can take it to their shop and I think they will try to repair first..If that doesn't give a result you can get a new one..
And about brands..I don't have too much experience with it, but listening from the people Asus is more reliable than Acer..That doesn't mean anything because I would buy Acer, somehow it is more unique and better for playing

I suggest you to google a bit and compare those two brands..
Asus owns Acer 
That you say, anyway not true..