I see a fire or injury in your future....your best bet is to consult the manufacturer of the heater coil. As Mr. Belson has suggested, the heater most likely has an imbedded thermostat which will simply cut power to the heater faster if you try to boost the voltage. That assumes of course that the heater doesn't instantly burn out from the excess voltage.
I would think that since it's tile above, the type of tile cement is crucial for proper heat transfer. You may end up having to lift the tile anyway.
What about the floor itself? Is it open on the underside? (like a second floor or built over a basement/crawlspace?) Could you insulate the bottom side to help avoid heat loss?
Please, consult the manufacturer, there are too many risks associated with your idea, and it would be unfortunate if someone got hurt!
Can you post the name of the manufacturer here as well?
