Hi,
I had the same problem with my multi three weeks ago. I left the car running at tickover for about 20 mins following a 30 minute journey, and didn't notice anything was wrong until I had a burning smell coming from under the bonnet.
Upon opening the bonnet, the radiator expansion bottle was full to the brim almost, and was boiling away quite happily just like a kettle!!!! But the cooling fan was not running, hence the overheating.
I switched the car off straight away, and left it to cool down. have covered about 500 miles since, and it runs just as normal, with no coolant loss or mixing of oil and water, so luckily does not seem to have blown the head gasket.
Anyways, back to the cause - the cooling fan. To test it, I would recommend removing it as it is so simply to take off.
1) Disconnect the connection plug, and unclip the cable from the clips
2) Undo the three securing bolts
3) Easily manouvre out from under the car (don't even need to jack up the car)
To test it, firstly sniff around the motor itself (will be a very obvious burnt smell if no good), and then place on top of the engine, making sure the blades can spin without hitting anything.
You then need to get two lengths of wire approx 1-2ft long with bare ends (insulation stripped back). Then simply connect each wire from one terminal on the battery to one terminal inside the plug housing on the fan. When the second wire is touched against the terminal on the motor, it should burst into lfe straight away - if it doesn't then it is knackered, and will most likely be the cause of overheating.
I managed to get a replacement on ebay for £25 including delivery. The one I got was from a Fiat Brava 1.2 petrol, Year 2002. It is the exact same part number as the multipla one. You would be best to supply the part number that can be found on the fan housing when buying a replacement, to make sure you get the right one.
One final note, when you have refitted the fan, be sure to check all the fuses that protect the cooling fan as per the car handbook. Especially important is the main fuse (maxi fuse rated at 30 amps) for the fan. This is situated on it's own on the bulkhead up above the battery inside the engine compartment. It's a bit tricky to find, hence I managed to boil mine over a second time while testing the new fan, and had not realised it had blown!
Sorry i have waffled, but I hope this helps, Tim.