The reason I'm thinking the problem might be a broken blend door, or blend door actuator, is that the OP says that his A/C blows cold at first and then stops working. The only way to know if the A/C system is working properly is by checking the pressures with an A/C manifold gauge set checking HIGH and LOW pressures with the engine running while taking into account the ambient air temp and humidity. This will tell you if your system is charged to the right level and if you perhaps have a blockage in the system.
Youtub'er fortechmakuloco has a 6-part series on diagnosing Ford A/C problems. It's worth watching if you really want to know how your if A/C system is working.
Tip: A/C shops are notorious for replacing perfectly good expensive parts and still not fixing your issue. The common first thing they tell you is that you need to replace your compressor. These unnecessary repairs can cost you over $1200 or more, and in the case of a blend door problem your A/C will still appear to not work, blowing cold at first and then blowing warm air.
We had a member here with this exact problem last year. I kept telling him to check his blend door operation, but he would not listen and spend around $1400 having a shop replace his entire A/C system part-by-part only to still have the same problem. Finally he had the shop check his blend door, which turned out to be broken. This is a fairly common problem on Explorers, so best to check this first. Your HVAC system is capable of putting out over 140+ degrees of heated air and only around 35-40 degrees of A/C cooled air. If your mixing hot and cold air together, guess which side wins?
I had this same issue on one of our 2000 Mountaineers years ago. Worked fine until the engine warmed up, the appeared to have no A/C. I found it had a broken blend door actuator motor.
