I have a baseboard electric heater that is 208 volts. My power supply is 240 volts. What will happen if I try to run m y 240 volt electrical supply to my 208 volt electric baseboard heater?

It will work, but...
It will be quite a bit hotter,
It will have a much shorter life span,
And it will not be code compliant.

If this is as baseboard unit I would not even consider it. Electric baseboards are super cheap and it would simply not be worth it.