After a quick search, I was pleased to learn that Someone already did the job for us!
Check the link for the complete calculations. It uses the color of the melting door to estimate the temperature of the door and approximate many values, like the material of the door and melting point. The estimates seem pretty good, with the lack of anything better.
What is the temperature of the metal (I assume it is metal, but it doesn’t really matter) door? Here is a shot of the door being cut (melted) by Qui Gon. I used the PhET simulator to match the color of the heated parts of the door to blackbody temperatures.
This seems pretty rough, but it is a start. One problem is that the screen captures might be a slightly different color. Oh well, it is close enough.
The final answer around 28 kilowatts.