Hello,
If the coolant is out, you have only one possibility: it has leaked. Hope that it leaked to the outside, but it also could have leaked for example through the head gasked into the engine. Which will be a costly repair.
The termostat need replacement if it's not working. It's job is to switch between 2 cooling circuits. The internal one when the engine temperature is lower and the external one with the radiator when the temperature is higher, to cool down the engine.
As for the parts compatibility, on the bottom of the forum banner you'll find a link to
ePER. It's the FIAT spare parts catalogue. The search window is top left of the screen. You can browse by models and categories. But I suggest to search with the VIN of your car, as by default
ePER will show only the parts that fit your car, assuming no one messed with it before.