The AC and heat on my 2006 Mustang has stopped working. As for AC- the air only blows cold when I first turn the car on or when the car is moving. If I am sitting in traffic or stopped at a light the air blows warm! As for heat- it only works when I have the car on for 20+ minutes and even after that will randomly turn cold again. Any thoughts on how to fix?? Thank you 
Can’t speak to the AC problem, but the lack of passenger compartment heat is likely from among
- faulty engine thermostat, leaking or stuck open
- Vent door problems
- clogged heater matrix
If you have a gauge for the coolant temp, check that to make sure the engine is heating up to normal operating temperature within 5-10 minutes of driving. If that looks ok, ask your shop to test the temperature of the hoses supplying the heater matrix at the firewall. Turn the heater flow on to max, but the blower fan to off. If one hose is hot and the other cold or just luke warm, there’s probably not much coolant flowing through the heater matrix, indicating a possible blockage.
There are a number of things that could cause problems like this and without car in hand it’s impossible to make much of a guess.
Regarding the A/C the first thing that need to be known are the system pressures on both the low and high side. This will (preferably) require someone proficient in A/C to check.
The car is 10 years old and it’s quite possible that there has been some refrigerant loss over the years. That can be considered normal.
As for the heater the first thing that should be checked is the engine coolant level and then after that the thermostat.
Do you check the coolant level at times? These engines have plastic thermostat housings that can be prone to leaking.
Make sure your fan is working. A bad blower motor resistor can cause similar issues.
My vote is a faulty blend door actuator that is allowing the output to swing in temperature regardless of mode.