Hi Jonsel,
Welcome to the forum.
With regard to the previous service history, do you have any documentation with the car to say what was done last time round? There is a chance that the timing belt may well have been changed in that last service in 2013 as it potentially falls within the 4 to 5 year limit for the timing belt (4 years for use in demanding conditions or 5 years in all other cases - this info is all in your service booklet).
If it hasn't been, or if you can't tell with any certainty, then IMO it is probably worth ringing up a few Fiat dealers and getting a quote on the 72k service with a timing belt change.
Now I completely appreciate others will say don't bother paying the main dealer rates and use an independent garage etc, but your particular case it might be worthwhile to give you peace of mind.
One tip I would recommend with that last point is going to the Fiat website and searching for a dealer using the Dealer Locator. By default it will search for "Dealerships", i.e. the sales dealerships. Click on "Service Centre" and it will list all of the Fiat service/warranty dealerships nearby. From personal experience these service/warranty dealerships (a) often charge significantly less than the all-singing-all-dancing dealerships, and (b) you might find their customer service is better too as they can't rely on selling cars to make money.
Hope this helps anyway