Not knowing the exact specifications of your electric heater it's difficult to give a clear answer.

The best answer is to to buy a Kill-a-watt or similar power measurement device and find out for yourself.

Your electric heater is going to be more efficient at converting electricity to heat than any computer you're running, but it won't also be generating bitcoins at the same time.

[edit] I re-read and see you said 'furnace', I thought you meant a wall-plug type electric heater, a furnace will be a little harder to measure.