There are 6 temperature sensors and 2 light sensors in the HVAC system. See attached pages from the shop manual on the sensors.
A scan tool is the easiest way to check the system from here on. It can reset any old faults. It can also recalibrate the actuator motors. It can read the sensor temp values. Any faults in the HVAC that it can detect probably will not turn on the dash service light to alert the driver.
A few other ideas to look at:
Check to see that temp control buttons are not stuck. This includes the buttons on the HVAC panel and the steering wheel.
While in A/C mode, try setting the desired temp to a low number like 66 deg. But don't set it all the way down at 60.
In the heat mode check to see if the left temp actuator motor moves any while varying the temp setting.
There is an air intake hole on the front of the dash (see sketch) that draws in air for the inside temp sensor. The suction at this hole should hold a small 2" x 2" piece of paper in place. If not, the aspirator hose may have become disconnected or plugged up.
If not tried already, disconnect the battery for a few minutes and reconnect to see if the system resets.
The sensors can be tested individually with an ohmmeter to see if they are working. If the outside temp reads correctly on the control panel, that sensor is working.