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