20 A seems like a lot to send through a 3.5mm header, those are usually rated for ~7A or less.
This seems like a hot water heater pump or something?
If this is a prototype, I would recommend using off the shelf components, and just Jerry rig it together for your initial proof of concept. Even if it isn't that pretty you just want it to prove that your system works.
BLDC motor controllers are not trivial to design, especially sensor-less controllers. Your best bet would be a 3rd - 4th year EE student looking for a senior design project; but they will not be able to produce what you want in a timely fashion, and it might not work in the end. If you want to pay someone to make that controller for you its going to cost a lot. I've personally never made a BLDC controller before, so I don't have a good feel for the time it would take to design one. I would guess ~100+ hours to design, fabricate, and test on a good day. So that would be in the range of ~$10,000 to get that done.
If I were you, I would use a RC sensor-less BLDC controller which you can get for $10 to prototype your system (like the one in the link below). Then adapt it to the system you want to use it in. (keep in mind these aren't designed to run continuous only for a few minutes at at time, so it wouldn't be a good long term solution.)
http://hobbyking.com/hobbyking/store/__13429__HobbyKing_30A_BlueSeries_Brushless_Speed_Controller.html
I still am not really sure what you are asking for, what are the temperature sensors pins for, are they inputs? Is the controller going to do some control functionality with it? Is it just passing the signal through? Is this switching heating elements according to temperature?
Tell us what is the application for this, and you might be able to get someone to help you pro bono.