  In a recent paper we introduced two Potts-like models in three dimensions,
which share the following properties: (A) One of the ice rules is always
fulfilled (in particular also at infinite temperature). (B) Both ice rules hold
for groundstate configurations. This allowed for an efficient calculation of
the residual entropy of ice I (ordinary ice) by means of multicanonical
simulations. Here we present the thermodynamics of these models. Despite their
similarities with Potts models, no sign of a disorder-order phase transition is
found.
