I'm assuming a Punto, with a FIRE engine.
If insufficient antifreeze, radiator can freeze, preventing coolant circulating, leading to overheating. Sadly, overheating these engines is likely to cause the head gasket to go.
Alternatively, head gaskets seem to be a weak point, usually some time after 60,000 miles, but usually a simple replacement without other work needed.
Rad fan may fail to operate, usually the sensor in the radiator.
Thermostat can fail causing this problem. Or the coolant cap itself.
Any coolant leak will reduce quantitiy of coolant, preventing proper flow. Look for signs of leaks, or do you top it up regularly? Topping up should not be necessary.
Diagnosis: Have someone else with you, to help, and in case of emergency.
Once its all cooled down, leave it overnight and attack it with fresh eyes, make sure coolant level is topped up, then start engine. Engine should get warm, them top hose from engine to radiator should get hot as thermostat opens. Radaitor should then get warm from top down, then bottom hose. Be very careful not to get hands near anything moving, especially the radiator fan that may cut in any time. Don't touch the exhaust, it will get very hot and will take the skin off your fingers.
Stuck thermostat will stop top hose getting hot.
Blocked (frozen) radiator will prevent circulation, so rad will not get hot all way down. (Difficult to diagnose now weather warmer, but if problem has gone away, frozen rad seems likely.)
Once running for some time, temp guage should get to normal, then as it rises a little more, fan should cut in.
Head gasket will likely pressurise the system, causing the cap to release the pressure.
Hope this helps and is not too late.
