Other than re-grouting, ceramic tile is not a material that lends itself to any sort of refinishing. However, as long as the base layer is secure (no loose tile, etc.) and the floor is structurally sound, you can easily add another layer of tile on top of the existing tile floor.
If you are mentally done with ceramic tile, another material you should consider is laminate flooring. Available in an unbelievable range of colors and styles, laminate floors are very moisture-resistant and a perfect choice for a bathroom makeover. Laminate can also be laid right over the old tile floor.
As for the heat question, if you are referring to radiant heat that is in the floor, this should not be a problem. If you have a radiator that is built into the wall, you should also be okay as long as you have at least 3/8 of an inch or so underneath the radiator to slip in the additional layer of flooring.
The only possible negative effect I can foresee is that it might be more difficult to get that radiator out of it ever had to be repaired or replaced. This, however, would be a rare situation since old radiators are among the most durable plumbing products ever invented!