Your example 2 is the correct one. If the pipe has lifted off due to themal loads then there will be no friction due to the uniform load as it is not in contact with the resting support. Example 3 does not consider the effect of thermal strain on your system and leads to incorrect results. The same can be said for Example 1. If the pipe is in contact with the restraint then you will see friction forces due to all the loads on the pipe (W, T, U).