We need model number on Furnace, AC, and Thermostat. Does the thermostat control both? Do you have 12 volt power, verified with a voltmeter? Does you monitor panel work? Do you have propane, verified by lighting a stove burner for 3 or more minutes?
Sorry, lot of questions, but we have little to go on. May also help to have year and Make and Model of your camper. Also keep a list of things you have checked, and why, and post them. For instance, why do you think the thermostat should have 7.5 volts?
One last thing, for the AC to work, you will have to have shore power, at least 30 amps, not using an adapter and plugged in to a standard wall outlet.
2012 Ford F250 ext. Cab 4x4
2002 Jeep Wrangler Sahara
2008 Yamaha V-Star 650 Classic
2008 Work and Play 18LT