Fred I own an 03 Town car, and if the interior is hot, left in the sun with the windows up, the interior gets over 120 degrees, I also have a thermometer in one of the A/C registers, the temp slowly comes down and like yours, it eventually reaches 40 degrees and cools very well. I did have a small freon leak in my receiver drier, Lincoln wraps it in a foam blanket, and they tend to rust out, My car only has 22,000 miles on it, and it rusted thru, the cure could be checking for a leak, and if found, replace the receiver drier, and recharge it at a shop with an A/C charging machine(station), this will vacuum the system, hold in vacuum to test for leaks, then recharge with the exact amount of R134a refrigerant. This fixed mine from mediocre, to top notch. Charging to exact specs is not possible with the hand held cans sold in parts stores, and this is critical, pay the money I did and I work on them!
Thursday, July 13th, 2017 AT 6:20 PM