having owned and sold lots of 156's this is what we have found.
The thermostats can get lazy with time and this has two effects, some open up slowly and can even cause the engine to appear to be overheating if, say you give it the beans before the engine has had a fair chance to warm thru...feel the two hoses going to the rad, one will be cold, one hot and you may loose coolant from the head tank!
Secondly failure, most never fully close which is more common and the engine runs too cool, this means the engine never runs as well as it could do with correct running temperature, the ECU will alter mapping timing/fueling etc to suit a too cool engine.
Don't bother with pattern thermostats, ALWAY fit a genuine Alfa part, the thermostats come as assemblies with the t/stat and cover for want of better words to save on labour costs, the genuine part can be bought for a little as £28 with VAT, maybe less, but is around £45 from an Alfa dealer.
hope this helps
My '01 156 1.6 Veloce has just had a new t/stat and coolant and settles right in the middle, and i mean in the middle