Need laptop $700 or under that will run all Blizzard games perfectly

Could somebody help me find a laptop with the specified budget that will run all blizzard games at max graphics with 50 or 60 fps?

Considering i am a picky butthole there are a few things i am looking for aside from the forementioned items.

Before i list them.. i would like it to be known that i currently have a 4 year old Toshiba Satellite. It is running slowly lately, and i do not like how it overheats and turns off a lot, i do not like it's shape, and it seems very un mobile. It feels like it's a hassle to take it in a backpack or something because it feels so big to be a laptop, it seems more like a replacement desktop to me. It has a 15.5 inch screen, and i would be looking for something a bit smaller perhaps 14 or 14.5 inches.

Picky items i am looking for:

-Doesnt get too hot.
-A very mobile computer
-14-14.5 inches
-Shape, i would prefer if, when closed it was just a rectangular prism shape, just like a closed box. flat on all edges.. (seems silly i know..) (If you don't know what im talking about, an example would be like the Google Chrome OS Laptop's shape)
-Will last 5 years running nicely if possible
-Has plenty of ram
-Is still useable for school because i will be going to college next year.

Thanks for your trouble, and if i am asking too much please let me know.

You can't find a laptop that can max out all of those games with your budget.
The cheapest gaming laptops cost $1000

They aren't but they still need a good amount of GPU power.

Do you know of any laptops specifically? Sc2 i dont really care about, but being able to run the rest would be a plus. Or at least give me a list of good stats i should look for in a laptop to meet my criteria. Thanks, Zeroslack.