If you can only buy from amzon, then you choices are pretty much limited. But still few good deals out there.
In terms of build quality and temperature, I would suggest sony or lenovo for this price range. Specifically you could get a core i3 cpu in a 15.4/ 14 inch laptop.
A 15 inch Sony VAIO EH2 Series
or a 14 inch Sony VAIO EG2 Series
The Lenovo G570
runs real cool. But the fan makes a bit noise because it either switches on or off. Its pretty much same for most laptops.
If you can buy from other sources though, its a completely different ball game.