In a normal incandescent light bulb, the filament is made from tungsten. Like you said, it undergoes large thermal strains because it doesn't start emitting much visible radiation until it reaches ~4,000°F (IIRC). However, since it needs to have such a high temperature to function, you can't really have a 'sufficiently cooled bulb', since it wouldn't emit any light.
So, the way I see it, you're right. If a light bulb were left on forever, it should never burn out. However, in practice, one thing is probably the main contributor to bulb burnout. Cyclic thermal strain (resulting from normal power fluctuations and/or turning the light on and off) fatigues the filament, generally causing it to become brittle. One day when it's heating up, the strain will be too much for it and it will fracture. Alternatively, if you bump it after it becomes brittle, it breaks.
I think this is probably true because of a couple anecdotal observations. At school, we always had lights outside that were constantly on (safety measure in university-owned housing

). These bulbs seemed to go out a lot faster than the indoor bulbs, despite the fact that they were always left on. This indicates to me that fluctuations in the bulb temperature (which could be caused by something as insignificant as a small change in the wind speed) cause rapid thermal strain cycling, leading to faster filament embrittlement. The indoor bulbs generally seem to go out after a long time when someone bumps them even very lightly. The filaments seem to be more sturdy after only being in use for short periods.
To solve this problem, we could use a material that has a near-zero coefficient of thermal expansion (CTE), as this would minimize thermal strain. However, not very many of these materials exist, and most that do don't seem to emit light when heated. The one that comes to mind is a carbon fiber-polymer composite. The carbon fiber actually has a negative CTE, so when it's mixed with a polymer with a positive CTE, they can cancel each other out if everything is done correctly. However, it doesn't matter how hot you heat it - it's not going to spit out any light for you.
Other alternatives would be to make the bulbs bigger or change out the argon filling with a less thermally conductive gas. This would insulate them from changes in ambient temperature and theoretically improve their life expectancy if my theory is correct.
HowStuffWorks.com article on light bulbs