I left my Bialetti coffee maker too long on my inductive stove. It got red hot for a moment and has now a nicely oxidized base. Is it possible or advisable to clean it so that it looks new?
Depending on how badly the item is damaged and how much you care, I probably wouldn't bother to do anything. A little bit of heat damage is not going to affect the function or durability.
If you did want to take a crack at it, Bar Keepers Friend is a cheap and easy-to-find cleaner for stainless steel items. You could try scrubbing it with that, per the directions. It's not particularly dangerous although it does contain a mild acid (oxalic acid) so you probably want to wear gloves. But depending on the extent of the damage it may not help much.
(FYI you said the item was stainless steel but aluminum is much more common for stovetop espresso makers. Aluminum is softer and should clean up pretty easily.)
Whether you have the silver/chrome base or the stainless steel, then unfortunately, no. The steel has lost it's temper (metallurgical changes) and it is not stainless anymore (it can rust now), and this aspect can't be cleaned or repaired. It could be refinished by electroplating it (not really a DIY thing, and although there are electroplaters for hire, the price would be hundreds of dollars).
On the other hand, I might suggest using a high temperature paint/enamel. The silver (spray) paints just don't make a good chrome finish (so I wouldn't suggest that); but other colors could work. You should not use paint on the inside of the coffee maker, and some of the high temperature paints (like manifold paint) need to be cooked for it to cure. So you should disassemble the coffee maker (remove any plastic) before painting and baking it.
If you decide to paint it, read (especially on the paint can) about surface preparations.
i am not sure what ben is talking about, but then again, i am unfamiliar with bialetti coffemakers. i am however, very familiar with stainless steel.
if this is just a question of removing heat discoloration from stainless steel, its pretty straightforward. your part is probably made from 316 stainless, but most likely 304 stainless. you may have changed its temper, but its hardness is not relevant. what is relevant is the fact that you induced a heat catalyzed oxidation of an alloy that doesn't oxidize easily at room temperature. either way, its the two steps below:
1) mechanically abrade the area with 400 grit silicon carbide or zirconium carbide sandpaper. sand the area in the direction of the preexisting line finish on the vessel (if its mirror polished, sand however you want until it looks like what you want - you can look up how to polish stainless elsewhere)
2) passivate the stainless steel by immersion in a 50% solution of nitric acid (careful, this stuff is dangerous - wear good latex gloves and a niosh full face mask for acids). this removes the free iron from the alloy and essentially resets the stainless quality of the metal. just immerse it for approx 30 seconds, or until the bubbles evolving from the surface start to spread out and stay on the metal, or stop altogether. remove from the acid bath and rinse in baking soda and water.