The 02 does have an IAT sensor. It's integrated inside the MAF. The other MY Mustangs have a separate IAT sensor located in the intake tube. Further proof there is an IAT sensor is right inside the ODB2 scanner.
The toubleshoot, cross check with reality. For example, if it's 70 degrees outside and the PCM says the IAT is -48, then you know something is wrong. Note, because engine bay temperatures are normally higher than outside air, it would be normal for the IAT to read slightly higher than air temperature.
As for the engine coolant sensor, it's a matter of cross checking the the values that the PCM has with reality. For example, if the motor is at full normal operating temperature but the PCM says 160 degrees, then we can conclude the sensor is wrong. Note, air in the coolant crossover can cause the ECT to read low.
If the motor is actually cold, then focus should be on a stuck open T-stat. The actually motor temperature can be determined by using an infrared scanning thermometer. Just point it at the T-stat housing.
I do agree that the cats maybe indeed toast. I'm just trying to push a slightly different trouble shooting path. IE, Test. Think. Start simple and work up. Working up can include staring with cheap/easy repairs just because they are cheap and easy. Then it makes it easier to justify the more expensive repairs when the other "possible" causes have been ruled in/out.