The laws of physics say you can't burn energy you don't have.

If you're restricting calories and your body isn't doing a good job of mobilizing energy from fat reserves, then one way or another you'll burn less energy. You'll fidget less, think poorly, turn up the thermostat, lack the motivation to exercise, and if you do get a little exercise you won't be very vigorous about it. No amount of willpower can overcome thermodynamics.