A late answer, and again, consult your local Rov:
According to Rav Yehoshua Neuwirth's Shemirath Shabbath, chapter 1, sections 36-37 and 60:
Any type of food, even uncooked, may be placed in a pot standing on top of another pot on a fire, as long as there is no possibility of the food reaching a temperature of 45 degrees centigrade/113 degrees fahrenheit. The intention of removing the food before it reaches this temperature is not by itself sufficient. It must not be able to reach this temperature no matter how long it is left.
Fully cooked food of any type that is still partly warm may be placed on top of a pot standing on the fire, even if it will reach a high temperature, as long as there is no chance of it roasting. It can be on the lid of the pot or in a pot on top of the pot.
Fully cooked solid food, even if it is cold or frozen, may be put on top of a pot standing on the fire, even if it will reach a high temperature, as long as there is no risk that it will start roasting. Therefor, cooked meat without gravy may not be placed on top of a pot on the fire, since it will now roast in the dry heat.
The ability to heat solid food is dependent on there not being anything (such as solidified fat or grease) that will melt when heated. This is due to the prohibition of melting on Shabbath. Exceptions: if there is only a small amount of fat which mingles with the rest of the food as it melts, this is permitted. Dissolving a sauce which is customary to each in a congealed state, such as fish sauce, is also permitted.
Since the above all talk about placing on top of a pot and not directly on the fire, you would need to using an inverted pan (or even a pot!) underneath any food that you are warming.