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The diffuse-interface model (DIM) is a tool for studying interfacialdynamics. In particular, it is used for modeling contact lines, i.e., curveswhere a liquid, gas, and solid are in simultaneous contact. As well as allother models of contact lines, the DIM implies an additional assumption: thatthe flow near the liquid/gas interface is isothermal. In this work, thisassumption is checked for the four fluids for which all common models ofcontact lines fail. It is shown that, for two of these fluids (includingwater), the assumption of isothermality does not hold.

Asymptotic reductions of the diffuse-interface model, with applications to contact lines in fluids