Laptops have lots of restrictions; mainly their limited upgrade options. Therefore, it is not an ideal solution to play games if that is going to be the only gaming device you will have. If you are going to buy a laptop for games, then I recommend spending a little more than you want to spend because that means you can postpone buying another laptop. Say for example, a laptop with a GT 650m instead of a GT 630m costs $150 more. Spending that extra $150 now can mean that instead of buying another laptop in 2015 when the GT 630m may no longer cut it for low graphic settings, the GT 650m may last you until 2017 when it may no longer be powerful enough to play games at low settings to make it enjoyable.
With regards to overheating, yes, laptops can overheat when playing games. For example, I bought a 14" Lenovo Y470 back in Sept 2011 which has a Sandy Bridge Core i5-2410m and GT 550m with a 1366x768 resolution screen. I wasn't specifically looking for a laptop to play games on, but since it was within my budget I decided to buy it. I have played some games on it and it does run hot. The CPU typically hits 90C - 92 when I play games like Mass Effect 3, Fallout 3, and Crysis 2. Pretty hot, but GTA 4 pushed the CPU to 99C and it started to throttle after maybe 1.5 - 2 hours of playing the game. The GT 550m wasn't so bad; 65C - 68C.
A cooling pad did not help lower internal temps at all; at least for the IdeaPad series. Lenovo calls the underside of the IdeaPad "thermal panels" and with good reason. I can put the overheated Y470 on my bare lap and it only felt pretty warm (not uncomfortably warm) so the chassis is definitely not designed to conduct heat. The only open vents were for the intake fans and you cannot force intake fans to draw in more air by using another fan to try and push in air.
Generally speaking, if gaming on a laptop is not a big priority, then yeah, a GT 630m should suffice to fix your need to play games if your expectations are low. I'm looking to replace the Lenovo Y470, not because the GPU is weak, but because I find that the 1366x768 resolution screen is too restrictive for my needs. Looking to replace it with a laptop that has a resolution of 1600x900 or 1920x1080 so that I can see more information on the screen at a single time w/o having to scroll around. Not sure if I'll get laptop with a dedicated GPU since playing games on it is not really a priority; I have my desktop for that.