Currently I have ten 60W incandescent light bulbs heating up my room, very little ventilation, and no ideas on how to stop them from making the room so very hot. If I had other lighting option, I would've switched to them by now, but I have to work with what I have.
How can I prevent the light bulbs from heating up my room, so that I don't lose too much light (at most 20% brightness loss is acceptable), and the lamps don't overheat, or otherwise become a danger?
You haven't mentioned what sort of fixture these bulbs are in, but this sounds like a classic case for compact fluorescent lights (CFL).
Efficiency in light bulbs boils down to "for a given amount of power running through the bulb, how much is turned into light and how much is wasted as heat?"
Fluorescent bulbs are much more efficient than incandescents; LEDs are even more efficient, but they're a lot more expensive. Here's a comparison chart from the US Department of Energy.
CFLs are marketed according to the incandescent bulb they could (theoretically) replace; 60-watt replacements draw 13 watts.
As I said, the replacement values are theoretical, and you may find that a 13-watt CFL is not quite bright enough; if so, you could step up to the "100-watt equivalent", which draws 23 watts, and still be generating far less heat than you are now.
The maximum-wattage labels in light fixtures are based on the power drawn and heat generated, NOT on the light produced; you could safely upgrade all the way to these bad boys (55-watt CFL, "250-watt equivalent") without worrying about overheating, but your room would be unbearably bright (and nearly as hot as it is now).
A 60-watt incandescent puts out about 800 lumens of light.
A 100-watt incandescent puts out about 1600 lumens.
Your 10 60 watters put out about 8000 lumens total. It'll only take 5 100-watt bulbs to equal that.
60 * 10 = 600 watts heat. 100 * 5 = 500 watts heat.
So, if the sockets can handle it, your room will be a little cooler if you switch to using 5 100-watt bulbs. The room will be just as bright. 150 watt bulbs, if you can find them, will give you still more lumens per watt.
P = I * A
Typically 10 or 20 AMP circuits draw :
10 * 120 = 1200 W
20 * 120 = 2400 W
Watts of power.
So, 600W is a lot on one circuit, (25% to 50%) of total output.
That in of itself will produce a significant amount of heat.
As @MT_Head says, you need to decrease your draw, and that is only going to be accomplished by switching out the bulbs to a more efficient bulb.
It will be more expensive. but that is the cost of efficiency.
