Surface temperature of a red dwarf star (e.g. Wolf 359) 2500 C
Melting point of tungsten: 3400 C
I find the idea of making balloon-like objects out of tungsten and gas, with a density less than that of the star's photosphere, and floating them around on the surface of a star to be intriguing. It would be a great location to put a heat engine. A totally sci-fi idea, I know, but still interesting to think about.
The only way of dumping heat would be to radiate it out to space, but "radiation" is a very inefficient way of losing heat. Unless I'm missing some really clever trick, soon your radiator will become about as hot as the surrounding gas, at which point the efficiency (= (T_hot - T_cold) / T_hot) drops to near zero.
* Not a physicist, so I might be wrong. :P
If the photosphere above the heat engine was opaque, then the heat engine would not work. So it makes sense to keep the heat engine near or above the top of the photosphere, without going high enough to overheat near the top of the chromosphere.
It's mainly just a fun idea. I have no plans of trying to build one in the near future. :)
* I am a physicist, but that is no protection against being wrong. ;)
I met David earlier this year at the NASA NIAC symposium, and spent a nice afternoon hanging out with him and Joe Haldeman and his wife. Very nice people! We toured the Swampworks and launch sites at KSC, and talked about practical methods for moving planets. It was a very enjoyable day.