Exterior temp off the chart, a/c not cooling

[politby]

So I have my first problem with my new-to-me 2003 Boxster S. Drove it home today and found the air con is just blowing air, not cooling (car has auto climate control).

And the outside temp reading was completely out of kilter. It started off at about 37 deg C and went up to 46, where it stabilized. Actual temperature was about 25.

There must be a connection. When I first test drove the car, everything was fine. During the week that has passed between the test drive and today, the seller has had the front bumper off to install an emergency trunk release wire hidden behind the tow eye cap, and he thinks he may have damaged/disconnected/dislocated the external temp sensor located behind the bumper.

Would a dysfunctional outside temp sensor cause an erroneous temp reading and make the climate control act this way?

Thanks in advance