I can understand a temporary heating, from the tital forces exerted on the moon but wouldn't there be cooling as well eventually when particles "give in" to contraction? Wouldn't they eventually net a unchanging whole body temperature? i.e. How can Europa's oceans be warmed by that and how can Io's crust be melted by that?
I think you've misunderstood both the nature of tidal stresses and the nature of the heating.
Concerning the forces there is tension in the radial direction and compression in both non-radial direction simultaneously present. If these forces were static they would do nothing, but they can change two different ways. In a case like Io or Europa the magnitude of both sets of forces grow and shrink as the moon moves around it's slightly eccentric orbit (thereby getting closer to and farther from the planet). In a case like the tides induced on the Earth by the moon, the primarily change is the steady progression of the tidal direction relative the body linked frame of reference that changes the stress on any given part of the body. In principle both effects can be present.
Concerning the heating, it arises from dissipative rather than elastic processes: think friction not rubber bands. That is to the degree that the body acts like a spring (simply storing the energy and gives it up again) there is no heating. To the extent that there is friction or fracture--irreversible processes--the energy involved becomes thermalized. The thermal energy can't go back into ordered bulk motion because of the usual thermodynamic constraints.