The way one could do it is to measure the current flowing through the cable that feeds it. This is not something to try if you do not know what the above means / do not already have a meter capable of doing it - perhaps an electrician or a friend can help?
The most likely source of problem is the thermostat that switches the mat on/off is malfunctioning. If it isn't that, then check to see if the mat is open-circuit - unlikely because you say it isn't working properly and it wouldn't work at all if open-circuit.