Admitedly - I do not own a Ferrari. Looking to buy my first one soon. But, my advice for what its worth (consider the price of the advice):
1. Start on the obvious/least expensive/least onerous fixes first. e.g. Check fuses, hoses, clamps, belts, etc.
2. If none of these bear fruit, move your way incrementally toward more complex/costly. e.g. radiator leak, water pump, cracked block/heads, etc.
Remember that the coolant system on your car is a closed loop. Therefore, you should be able to find the "symptom/s" easily. Also, something had to cause the closed loop to stress and ulitmatley "break." The challenge is finding the source. For example, replacing a ruptured hose may fix the symptom... but finding a faulty thermostat will cure the problem. Be sure to do an exhaustive anlaysis AFTER you found the symptom/s... and don't stop looking after you found just one symptom or cause. There may be several.
Hoses and clamps are like everything else in life - they wear over time... so a hose itself could be the cause. My point - just make sure that you are comfortable that you have solved the problem/s. A good test will be to run the car at idle for 10-15 mins in your driveway after putting the fix in place and monitor the temp closely. I do not trust gauges in cars exclusively, so I use an infrared thermometer when I work on mine... and will scan the entire cooling system to see what's running hot and what's not. This is always an interesting educational exercise...
Based on the fact that the car ran fine after it cooled down for some time provides some hope that it may not be too serious. Good luck.