Part of the reason that chocolate is so irresistible is the way that it is made up of a variety of fats, both from the cocoa bean and in many cases milk or even vegetable.   These fats happen to melt at just below body temperature so the chocolate melts in your mouth.  This is why chocolate is so obviously a bad material for making teapots, hence the phrase "as useless as a chocolate teapot"!

However,  James called in to the show to ask how thick the walls of a chocolate teapot would need to be to be able to brew tea in it, so in the best tradition of Kitchen Science, we set out to find out the answer to this critical question.

The obvious way to find out how thick you would have to make a chocolate teapot is to make a series of chocolate teapots with walls of various thicknesses and test them by brewing tea.  However this would take rather a long time and involve truly stupendous amounts of chocolate (as opposed to just ridiculous amounts).  We decided to do a series of tests on a small amount of chocolate in order to find out roughly how much we would need for the teapot.
Chocolate is a very complex substance and it doesn't melt in a simple way - it goes through a series of stages where it becomes gradually more fluid.  The teapot could melt enough to become flexible and then the pressure of the tea could cause it to distort and empty its contents onto the floor, without actually melting through the walls.  This means that just finding out whether it melts or not isn't very useful.  So we needed an experiment that modelled being part of a chocolate teapot wall as closely as possible, while using a sane amount of chocolate.