I spent all day on a car with this problem, except inverting the sides; right side (driver) and rear was warm.
Although this is a 156 all car makes might have this issue:
Take off the central top air vent to reveal the flaps. Observe flap operations (dual zone has 2 sets of flaps, direction and zones deeper towards the a/c evaporator). (optional) Use fiatecuscan to check for % flap opening/closing. Etc. See if both zones' flaps are the same position when the same temp is requested.
So far in my case, all was operating OK. But using a light you can see the evaporator.. left side (cold) was condensing like crazy. This can indicate insufficient pressure, insufficient gas, faulty evaporator... Check low and high pressure while system operates and use recommended values. In my case, the low pressure is OK but high pressure was 2x too low (125 psi, I think should be 250 psi). I'm told that the gas is enough in the system, but evaporator unit is faulty and we'll try changing it tomorrow.
My understanding is that if the gas is insufficient, it will get really, really cold but on a small portion of the evaporator. The portion immediately where the gas enters the evaporator, which results in very cold left side and nothing on the right side (in thai facelift 156's case)
PS: Sorry to revive this thread but I don't think nobody mentioned that before.
PPS: THE A/C IS REALLY DARN HARD TO TAKE OUT