I've got a 2000 F53 and the 3/8" is correct.
There is nothing wrong with installing a temperature sender in the cooler line. In the opinion of those that are considered experts it is the best location for temperature measurement. Below is my info on the topic from another forum:
I used this one in my 2000 F-53.
Transmission Temperature Gauge
It is the only one I found that is full sweep, that is, the gauge is sweep is a full 270?. The range is 100 to 280 degrees temperature, black face and red dial. I just went to a good auto parts store and got a brass 3/8" T for the install.
It has two bulbs, one for the pointer and one for the gauge. All the dash gauges on mine are illuminated with green light. Make sure you get the right color
light diffuser for the gauge so the it will have the same color light as the rest of the dash.
The only thing I would do differently if I had it to do over again is mount the gauge on the right side of the dash instead of the left because of the glare and reflections from the window.