We want to put ceramic floor tiles over a cement floor that previously
had radiant heat (not in use) installed about 50 years ago. My
question is, would the floor need extra thermal insulation between the
thermal tiles and the cement floor. We live in New York which can get
pretty cold in the winter. In general terms how much heat will we lose
across 500 square feet. Is a cement floor like this designed with
insulation in mind? Are their any mortors that provide themal
insulation?

Although I cannot directly answer your question, I can offer some
advice from my experience.

I have recently installed ceramic tiles in a home with radient
heating(in use). We put down cement backer board upstairs, installed
the tile downstairs directly to the concrete floor.

In my previous house, we had the same tile installed directly to the
cement, without radient heating. It was a bit cold in the morning, but
nothing too drastic. I live in North Idaho, so we do get a bit cold.

I would think that insulation would not be required, and here is a
link with info on the two different types of backer boards(mostly used
for floors that need reinforcing, as the main function of the backer
board is to provide stiffness, so no cracking may occur).

Forgot to add the link:

http://www.askthebuilder.com/199_Cement_Backer_Boards_-_The_Best_for_Tile.shtml

Small cracks in concrete could be caused by the seasonal movement of
the slab. To keep these movements from cracking your tile have an
isolation membrane installed over the concrete. This is a thin
rubber-like material that will protect the tile from the movements of
the floor, along with protecting the tile from temperature and
humidity changes.

http://www.screwfix.com/app/sfd/cat/pro.jsp?ts=91647&id=72451

UK, so not much use to you but it's the kind of product you might consider.

Best