Taurus AX4N hard 1st-2nd shift warm, cold is fine

I've ran into this problem a lot with the AX4N's. You're either going to have a bad manual lever switch, a worn bore in the valve body or a worn seal in your foward clutch piston.

How many miles do you have on the car?
Do you have any DTC's(Data Trouble Codes) stored, and if so, what are they?
Did this problem start right away or did it gradually get worse over time?

If you could answer some of these questions, I could Probably figure out which one is your problem.

I doubt very seriously you have a bad torque converter, It's possible, but you would notice it all the time and not just when it get's warm.

Does that mean rebuilt tranny?
180k
The engine light doesn't come on and I've never had it scanned. But it works, it flashes on when the cluster panel lights up on start
It's been like this sinse I have owned the car, for 3.5 years. When I bought it, I drove it very slow and didn't hammer on it and it was cold at the time so I didn't really notice an issue until it was mine.

The car acts fine when cool. Wouldn't a worn bore or seal act up when cold also?

There is a control wiring harness that plugs into the transmission. Unplug that connector & clean the contacts if they're dirty. Free and easy. Also try adding an additional stacked plate cooler to your transmission. I've been able to avoid the hard shift when hot by putting the transmission in neutral at stop lights to prevent heat build up from friction.

If the above don't solve your issue, the first things I'd suspect would be a bad solenoid for the 1-2 shift, or a bad transmission fluid temp sensor, or faulty programming in the PCM that may need an update. Ford was very tight with some of their programming (example: the O2 sensor tolerances in the Contour. That car threw a lot of codes) and this may be the case. If the trans temp is reading high, the PCM may default to an over-pressure 'limp mode' to protect the clutch packs.