Can you do it? Let me come clean and say you are not going to get a straightforward answer here. But if you want to be confused at a more profound level you have come to the right place.
I have personal experience of using a badly corked wine to deglaze a pan, so I know that does not work. I was hoping the heat would evaporate the TCA, but the resulting sauce was disgustingly corky. I mentioned this on a wine forum, where it was pointed out that fats bind the TCA and no amount of subsequent heat would get rid of it. I later discovered that cream is sometimes used to clean up corked wine on a large scale. The cream attracts the TCA and is then removed by filtration.
It was suggested on the forum that if you are going to use corked wine for cooking it is important to drive off the TCA by boiling it before allowing it near animal fats. Since then that is what I have done, and with positive results. It has not yet really been a strong test of the theory because I have only tried it with mildly corked wines, but it seems others too have had success by boiling first.
There’s only one small problem with this. Contrary to what most people seem to think, TCA is not very volatile. In fact its boiling point is about 250°C at atmospheric pressure, and below 60°C it is actually solid. So on the face of it, boiling wine is going to concentrate the TCA because there will be less alcohol and water after boiling.
But it is more complex than that even. TCA is soluble in ethanol, but not very soluble in water. So as the wine is heated, the alcohol will boil off before the water, and the TCA previously dissolved in the alcohol will be thrown out of solution. And it seems that as the liquid cools below 60°C it will precipitate as a solid. That might explain why boiled corked wine does not smell of TCA. But then wouldn’t fats from cooking redissolve the TCA and make things taste nasty again?
There are another couple of possibilities that might explain why boiling works. One is steam distillation, which will allow a liquid to boil off below its normal boiling point, though I am not really sure I understand how much agitation is required to expose some of the minute quantities of TCA to the surface to allow this to happen. The other is that heat may cause TCA to undergo a chemical reaction that results in a less nasty reaction product.
Ultimately, if boiling corked wine works it works, but I personally don’t think I have enough evidence yet. It does not happen to me often, but next time I have a moderately or badly corked wine that I cannot return I shall try boiling it for use in cooking. If you do the same, let me know how you get on. Also if you have any theoretical contributions. Science will not advance itself.
Update 28/03/12: I have since seen that several people have reported successfully using corked wine for cooking in various ways, including deglazing pans to make a sauce. It occurs to me now that maybe the important factors are how badly corked the wine is to start with, and how strong the other flavours in the sauce are. Also, in my bad expeience I think I reduced the sauce a lot, thinking I was driving off the corkiness, but that maybe concentrated the TCA, as you might expect bearing in mind its boiling point.