Lighting, Light Fixtures, Ceiling and Exhaust Fans - Speed control of small duct booster fan

I have a wood burning fireplace in my gameroom, I recently cut a hole in my floor and installed a grate in hopes of circulating some of that heat upstairs. I would like to install a small duct booster fan in my bulkhead to draw that air up thru the ceiling to the upstairs. Can I install a ceiling fan type speed control...not a lighting rheostat...on this fan to control the speed of this fan? The fan is a standard duct booster fan available at all of the DIY home center. My thought was to control the speed and the noise since it feeds into a living space and not really confined in a duct where it would attenuate the sound. Thanks, Lynd