I doubt that it thinks it's -40F when the ECT goes out; however, it does probably go to a default set of data that's designed to at least allow the car to start and not strand you.

First place to start is by getting a functional ECT in it, then see what happens. During the install, you may want to disconnect the battery and kill the KAM (keep alive memory) of the computer for three reasons. 1) Good practice anytime working under the hood; 2) It will clear the old codes out; 3) It will also clear out any adaptive strategy the ecu has 'learned' while trying to cope with a bad ECT. If you don't clear it out, drive it for a while with the new one while it 're-learns' what it's like to be operating with a properly functioning ECT.