fans & temperature

could anybody tell me if its possible to connect a pc fan to a dc 9v or 12v adaptor as it tells you the fan connects to the motherboard? i need to get my grow cooled as its getting too hot and im lookin for the cheap version of just extracting the hot air direct from the light
i already have fans and an extractor but because its quite enclosed it still really heats up.
the kind of fan im after is a couple of ball bearing pc fans as these are supposed to be really quiet and reliable but i looked up ballbearing pc fans and it says they connect to the motherboard with 3 prongs
can i just connect the fan to a dc 9v adaptor even though it says it connects to the motherboard?

how big is your grow space? (inches will work perfect info for me)

36inch by 48in height 6"3 i have a normal bathroom ceiling extraction to my loft but it doesnt seem to be working that good its ok for the smell but doesnt take enough heat out of the area
if i leave the door open a bit it stays under 86f but if its closed it rises gradually i know it can be ok in veg even better for it to be warmer but its when im in flowering i want to maximize my yield ive already been growing in the conditions for my last crop but i want to maximize my yield