i got my laptop with dual core turion II 2.4ghz and HD5650 1GB, 3gb ram(cheaply upgradable) and 500gb hdd, ~550$, but over year ago, may be cheaper now.
sure, the cpu is much slower than a i3, but dedicated vid card can run casual games very well and im even able to play most of new games.
overheating is bit of a problem indeed, it often runs hot, but with bit of a effort ( undervolt + additional cooler ) you can get it cold enough, and it has never crashed due to overheat or anything.
not sure is there deals like that in other countries, but search for Acer 5552G.