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.