Having spent many years as a jeweler and metalsmith, I can tell you it's a matter of 2 things, (1) the speed of your buff, and (2) the compound you use. Warming up the metal has no effect.
Stainless is a hard metal and so you need a lot of speed on the wheel and you need a strong cutting compound. Consider the cutting compound like sandpaper. It's used to smooth out very fine, and sometimes not so fine scratches. After that, you use either a white diamond or red rouge polish to brighten it. Never put two different compounds on the same buff.
Keep in mind that you should always keep the piece moving, especially when using cutting compound, otherwise you'll risk "drawing" the metal (wearing grooves in it). And when doing your final polish, keep changing directions, it'll give you a nice bright shine. You can finish by washing the piece with slightly diluted sudsy ammonia. It's the best at removing the compound film and buildup from the metal.
I just polished my glass trim a couple months ago, and they came out very nicely.