It wouldn't break the bank to get a new temp sensor from Fiat and fit that anyway. I tcould be a warm-up issue.

But get the damn thing diagnosed and clear the errors from the ECU. Then you'll start making sensible progress instead of just guessing and asking everyone else to guess...

get a multimeter!
you can use it to messure most of the sensors.
the temp sensor is quite cheap ~10 euros.
it can be tested with an multimeter on the ohm scale. it does light up the check engine light if faulty.
BUT THE ENGINE SHOULD STILL START AND RUN

as everyone said : DON'T buy, CHECK!