Yeah - the lever on the valve might be moving, yet the valve itself may not be! You should be able to unseize it (see below) but you will have to take it off (not difficult).
I've fixed this many times. There are two types of valves - white (small, sort-of rectangular), and black (large, kinda mushroom-shaped). To make matters worse the official FIAT name is 'COCK'. Need I say more?
Removing the valve is simple - get a plastic bowl and jam it under the pedals. Undo the hose clip on the valve. Undo two 10mm nuts, and pull the valve off.
I'm assuming that yours has the white valve.
The black type is much better because it has a rotating disc inside, with a hole. The white type has a sliding 'shutter' that gets hopelessly seized. Well not hopelessly - I fixed mine by boiling it up in a saucepan and shoving in a screwdriver (the shutter has small holes near the end). You also need silicone spray or similar to get it moving again.
I actually bought a new, black, valve but found it wouldn't fit in my Uno Turbo due to aftermarket a/c. So if you do spring for a new, black, valve, you will get a better one than you probably have. Another improvement - the cable fitting slides in the lever, so much smoother action. More progressive heat control also. The black valves don't seem to seize/break so I recommend you find one of those in a breaker's.
Remember to put green stuff in the radiator when you've finished...
-Alex