I know the station's solar panels rotate to track the sun (and also rotate to be in-line with the station for lower drag on night passes), but how does the station itself rotate? I imagine it has to rotate for thermal management issues, or maybe not? I also believe it rotates for docking/supply ship approach, but I'm mostly interested in how it rotates for thermal management. Which axis? What's the rotation rate?
Most of the time (when it's not maneuvering for experiments and/or visiting vehicles) the ISS maintains a "fixed" attitude in the noninertial Local Vertical, Local Horizontal reference frame. This means that it rotates about the Y body axis (the "port / starboard" axis) at a rate of one revolution per orbit, about 0.067 degrees per second.
For easier reference, here's the International Space Station’s coordinate system (image credit: NASA):