It's how the ecofans work, although they are a bit pricey!
Ecofans are pricey, but I have to say I think they are truly awesome. I have one on my stove, and it works wonders, especially because the stove sites in a fireplace recessed beneath a chimney and thus a lot of the heat would just sit in the alcove unless it was actively being pumped into the room. I think my small (not headroom for the large one) ecofan is one of the best investments I've made, and I'm definitely ordering a second (larger!) one when we get a second stove for the room next door.
I found them fairly cheapish on ebay
