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There is a good chance your heater core is blocked. These ford taurus's are extremely common for the heater cores geting blocked.
A good way to tell is with the "engine hot" grab the heater hoses, they should be both hot abd the exact same temperture. IF one is hot and the other is cold than you will have to replace the core or try flushing it.
IF you want to try and flush it, remove both heater hoses, flush with a garden hose both ways back and forth in opposite directions to dislodge any gunk in there. you will notice the flow increase with more fflushing. IF it only gets warmer and is so plugged than it will have to be replaced.
IF there is no blocked heater core and you are sure that the blend door actuator is working then you might have broken door and the only way to inspect it is to remove the box assembly.
but i would start with a core flush
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