I have the same drier model TC71 with the same fault, (i.e. no heating any more). I cured it about 18 months ago by replacing the one of the 2 button theromostats located inside the rear of the machine . They look like thick silver buttons. Just remove the large cowling plate & you'll see them sitting above the machine heater elements,. I'm assuming the elements are OK. These thermostats retail at about £9 each and can be purchased at most white goods repair centres.
Don't forget to isolate the electrical power before you do anything.
Unfortunately I got the same problem last week again and its not the thermostats this time. If anyone knows what else can cause no heating besides the thermostats or the elements on the Hotpoint TC71 please let me know.
Des Gilmore, January 2006