No you cannot plug a 100v into a 120v outlet, it will fry whatever the product you are plugging up.
You might have a problem as the dryer plug also carries a neutral with it. What type of plug is on the heater right now?
Do this electrical work only if you feel confident that you can do it safely. If not then this is the procedure that an electrician would use and you would be able to follow what he is doing. Again...
Check out the home electricity part of this page, this question gets anwered several times in there. Good Luck.
yes