I had a simiar idea a few years ago. I bought a box of quiet computer fans from a surplus dealer, hooked them all in parallel to a husky wall-wart power supply, and put them behind and beneath the hot-water radiator in the kitchen to push more air through the radiator and to improve the circulation of warm air in the room. It made a slightly-perceptible difference in the room temparature, but it was definitely noticeable when next to the radiator -- a spot favored by the cat, whose fur accumulated on the fans and necessitated occasional de-furring ;-).
In an older home near Ottawa we had baseboard hot water radiators, and the air temperature was very inconsistent in different areas. Improved that by installing vents in the floors at opposite ends of the house and running 4 inch fans constantly - the kitchen and living room ends blowing down into the basement, the bedroom ends blowing upwards so that the air was always kept in circulation throuout the house. Much more comfortable after that.
Newer homes in North America (at least up here in Canada) use forced air heating (amd cooling). That is we have a natural gas (normally) furnace in the basement and warm air circulated though the house in ducts and feed into a room through an opening called a register. Since we have the ducting, airconditioning is frequently added to the climate control.
There are some products that are similar to in idea to Radfan, and some that might even be integrated into the IoT.
I actually built my own register booster fan- my employer makes power supplies with cooling fans so we have many knocking around. So a fan plus power supply was simple, but it didn't seem to make much difference to the room temperature. I could've entered it for a remarkably short presentation in the gadget smackdown at EE Live.