The previous answer is correct. The Expedition does not use a heater control valve to regulate flow through the heater core. Ford did do this on the later model Explorers, but not the Expedition. The Expedition uses the same plenum box/heater core as the Ford F150 pickup trucks and as the Lincoln Navigator, so any information you find on either of those models will be directly applicable to the Expedition.
It sounds like the immediate problem is that the two heater cores are not heating up. You need to check that the radiator is full, not the overflow tank, the radiator. Open the radiator cap on a cold engine and check the level. If air gets trapped in the radiator, it can have significant impact on heating. If the levels are OK, I'd try a good radiator flush next. Prestone makes a good diy kit and has chemicals to do a thorough clean. Any oil change franchise should also be able to do this. If it's just the heater core, you can disconnect the two heater hoses and flush both cores independently with a water hose and hose repair connector. You should be able to feel the two heater hoses from a cold start and feel the hoses warm up at about the same rate and get uncomfortably hot.
It's actually more common for the problem to be with the blend door system. This door directs the air flow through the heater core and regulates the temperature of the air flow. It's common for this door to break, losing control over heat. The door is on a vertical axis(like your front door) and can swing back and forth at random or wedge in a set position. It's an expensive repair to remove the dash and plenum box to get to the door, but there is a diy kit that will let you do the repair without all the work and expense. Check for a video posted on YouTube that will show you how to diagnose and repair the problem. Searching "expedition heater" will get you to the right place.