Will this help my system?

oh, please tell me if this will keep my system any cooler:
(red is the fan I wanna put on, and the black is the stock heatsink and fan, heatsint is about 2" deep, so there is lots of room for the fan)

Please don't make fun of the pic, but this computer at my school onlyy has MS paint
(red is the fan I wanna put on, and the black is the stock heatsink and fan, heatsint is about 2" deep, so there is lots of room for the fan)

Please don't make fun of the pic, but this computer at my school onlyy has MS paint