How to prevent incandescent light bulbs from heating up the room, safely?
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).