I pullled the instructions for removing the heater core from our service manual and attached them. You will note that is says a linkage must be removed that actuates an air blend door on the heater core case. It is removed by removing a spring and pushing the linkage ramp pin so you can move the linkage arm.
It is the only thing I can find that sounds like what you are describing. I also double checked on you tube, a Ford enthusiast forum and on a few places on the internet and could not find reference to a plasitc piece in that area. You may be confusing it with another blend foor actuator that does have a plastic piece on it or there are several plastic components to remove around the actuator, I found this information in a semi-relaiable place, that you may have gotten confused withe the air door linkage parts. The information on the internet is so incomplete and confusing that I could have easily mis-understood the reference to the plastic piece as well. So, I believe this may be the case.
To clear this up I am attaching you the removal instructions for the heater core which include the linkage for the air door and a diagram named, "FIG 5" which is referenced in the instructions.
The instructions say the the instrument panel must be removed to remove the heater core. However, I found a video on You Tube that has a work around to cut off several hours of labor and avoid removing the instrument panel. You simply lossen the whole dash and pull it back enough to get to the heater core. The video is for a newer Taurus, but I looked at other Ford heater core videos and they share a lot of common design when it comes to getting to the heater core as other models used the same work around to do the same thing. So, you should look into this for your car even though it sounds like you are past the point there this would be beneficial. If you still want to see the video, the URL iis below.
Let me know if this clears up the confusion.
Images (Click to enlarge)
Saturday, November 3rd, 2012 AT 6:23 PM