Fiat spent thousands - ok, well, maybe tens of pounds designing the cooling system.
The panda cooling system is primitive and typical of systems designed 30 years ago. Modern cooling systems have manifold heat exchangers to quickly warm the coolant, and active airflow control through the engine compartment to manage underbonnet temperature and allow the engine core to heat up faster.
Not sure there's anything to be gained by blanking it off. The thermostat will only open at a set temperature, the radiator isn't in play until then.
It's nothing to do with airflow through the radiator; that's irrelevant to the warmup time as the thermostat will not allow coolant to flow through the radiator until the coolant reaches operating temperature. What matters in determining the warmup time is controlling the flow of cold air through the engine compartment, something which the standard Panda cooling system does not do.
I'd agree that blanking the radiator itself is pointless; but blanking the grille, especially the part that's not in front of the radiator, will significantly reduce the warmup time.
They aren't overcooled at all.
The engine is massively overcooled for the UK winter climate. It's designed to cope with the worst case scenario of hard driving in a southern european summer.
If your car has air con, you know you need air flow to the system too?
Airflow through the front grille is not relevant as far as the A/C system is concerned; cabin air is never taken from the engine compartment due to contamination issues; that's what the vents below the windscreen are for.
Cars with modern cooling systems incorporating manifold heat exchangers and active airflow management will typically warm up in about half the time of a Panda.
I did some experiments with blanking the front grille the first winter I got my Panda; I managed to achieve a significant reduction in the warmup time, but you do need to be careful not to let underbonnet temperatures get too high as you might damage the wiring and electrical components. Don't just rely on the temperature gauge as that is only measuring the coolant temperature. You would have to try very hard indeed to get the coolant to overheat; but my initial trials showed that underbonnet temperatures get excessively high long before this point, so do be careful if you are going to experiment - a fried ECU will cost you much more than any fuel saving you might make.
On cars used mainly for journeys <10 miles in a typical UK winter, improving the efficiency of the cooling system will likely get you a substantial improvement in both fuel economy and engine wear.
The real problem is that the cooling requirement during the warmup phase is completely different from the cooling requirement once at operating temperature; without some kind of variable geometry airflow system, you can't optimise both.
Front grille flaps, adjustable from inside the car, and a suitably located underbonnet temperature gauge, would make a good DIY project.