An interaction between conduction electrons is derived based on the s-d interaction model for dilute magnetic alloys. The interaction results from a process in which the first electron excites a localized spin and the second one deexcites the same spin. Thus it is a consequence of the dynamical character of the s-d interaction. Special circumstances for dilute alloys make the interaction large and we find that the thermal mass of the conduction electrons, when the electron-electron interaction is taken into account, becomes several times larger than the free mass below the Néel temperature. This seems to account for the anomalous specific heats of dilute magnetic alloys.