Conformal Mapping: mobius transformation, circles, and temps

I am getting my butt kicked in this particular topic of complex analysis. I have a certian problem that I have no idea how to even begin.

Circle #1 is centered at 2 + 4i and has radius 6. Circle #2 is centered at 20+6i and has radius 6.75. Circle #1 has temperature 0 degrees, and circle #2 has temperature 1 degree. What is the temperature at z = -10-8i

Click to expand...

I know I have to use a mobius transformation, but that is part of what is killing me. I'm not entirly sure how to set it up into a problem I can solve. The transform isnt the end, however, because I need to actually solve the system to find the temperature at a point.

Any suggestions would be helpful.

Thanks.