When a solid wheel rotates about a fixed axis do all of the points of the wheel have the same tangential speed?

Yes they should all be going the same speed.

Hope this helped :)

No - points with different radial distance from the center will experience different tangential speed.

Explanation:

Picture two points on the wheel: point A is very close (say, 1 mm) to the center, point B is further (say, 1m) away from the center. As the wheel makes one whole turn (2pi), both points will follow a circular trajectory, but point A will have traveled (2pi)x(0.001) meters and point B (2pi)x(1) meters in the same time. Point B's tangential velocity is therefore 1000 times greater than that of the point A.

The formula for tangential speed is as follows:

v = (angular velocity in radians/s) x (radius in m)

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thermal energy is the answer