Correct, the last 10 - 15mins blow cold. If it didn't you clothes would be piping hot when the dryer stops and the machine would catch fire sooner rather than later. The cooling cycle is very important.
You need to confirm if the heating element or thermostat is faulty. Frankly your repairman should have done this. An easy way to check if the element is functioning (without dismantling anything) is to buy a cheap digital wattmeter (a socket type used to monitor power consumption). Plug your dryer via the wattmeter into the mains socket. At the start of a normal drying cycle the heating element should draw around 2000 watt.
Mike, October 2009