Accurate temperature as in you read resistance and it corresponds to temperature, or as in your car tells you its whatever temp (or quite close) that it is outside? If its the latter, its cause the car is reading the MAF for the temperature now, as opposed to the outside air sensor. If its the former, then it means that the sensor is good, but you have a problem in the wiring (because you said the sensor is cracked, I think you mean the car tells you accurate temp..)

Pull your spark plugs wrt the stalling. I'm betting they are black, from running too rich. How many miles have you driven since you replaced the MAF? I wonder if the rich condition (your P0172) is still unresolved. This could be caused by a vacuum leak somewhere in your intake system. I wonder if you unplug your MAF and drive around if it will still stall on you. Supposedly it calculates the intake manifold pressure and rpms to calculate flow. This won't get you around emissions testing, but if its before the MAP sensor (so that the pressure is what your engine sees, as opposed to your intake manifold leaking) it shouldn't stall.. If you've only driven 30-40 miles try taking it on the highway 30-40 more miles without using cruise. That will help the tests finish, and highway engine speed tends to make it more difficult to stall. If the P0172 comes back, you'll know the cause of the stalling.. If you take the MAF off, do it engine off key out, and expect another couple of codes to come up as it'll tell you the MAF is unplugged...
--
If you're not driving it "like its stolen," are you really driving?