What's an HD rheostat?
I can't say much without knowing more about the type of motor and speed controller the router uses. If the motor is an AC brushless, then the control would have no effect at all on the heat output. If it's a DC motor, then it might work great - or it might blow up the speed controller, depending on how it's designed. I'll spare you the details unless you really want an explanation.
Don't use a rheostat, they waste too much power. Variacs are too expensive and bulky. I would use a triac. I almost did this recently, but found a free electric stove that someone was throwing out, so there was no point anymore. But, if you're any good with a soldering iron, you can build a very cheap, very simple controller that would work great with a heating element. It's the same principle as a light dimmer switch. The triac connects and disconnects the element to the power source on and off at 60 times a second, and varies the amount of power by changing the ratio between time spent on and off. I think a lot of electric stove-top burners use this method. If you're interested, I can show you the plans that I was going to use. The parts were going to only cost a few bucks.