Computer room so hot

Just having fans going means all the heat generated in the room is distributed well, but still trapped in there. You need to remove the hot air and replace it with cooler. An exhaust fan to move it outside will certainly help, but that means some other air will be sucked in to replace it - from where? Most likely from somewhere else in the house, and that , in turn, means more outside air will be sucked into the house in another location. Now, if your house has AC running the inside air flowing into your computer room will be cooler and you will succeed in reducing its temperature - good, right? But is also means the outside air drawn into the house will have to be cooled, raising your costs for AC. OK, "there's no free lunch" and you have to expect that cooling the computer room will cost something. But I suspect that is why friends have told you exhausting warm air out a window is a bad idea - because it increases costs of AC for the house.

If you ONLY want to cool that room, another option might be the "portable air conditioners". The are smaller units on wheels that connect both intake and exhaust air flows to a window by large-diameter flexible hoses. A unit like this with hoses long enough might be put into your computer room and connected to that window so that it cools only that room.

If you have no AC anywhere, the exhaust fan can still work if the rest of the house is cooler, but you must realize that the result will actually raise the temperature in the rest of the house slightly whenever the outside air is warmer than inside.