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The difference between the specific heat of a dilute [sup 3]He-[sup 4]He mixture and the specific heat of pure superfluid [sup 4]He at temperatures below the superfluid transition temperature is usually explained by considering the [sup 3]He as an ideal gas of quasiparticles with an energy spectrum that is not quadratic in the momentum, but which is difficult to justify on a theoretical basis. On the basis of a polaron-type model, introduced by three of the present authors, the specific heat of the mixture can be calculated, taking into account the emission and absorption of the phonon-roton excitations. In a temperature range where the [sup 3]He particles follow Boltzmann statistics, we find that the model accurately explains the experimental data for the specific heat. Therefore, the difference between the specific heat of the mixture and the specific heat of pure superfluid [sup 4]He can be explained as the result of the interaction of [sup 3]He with the excitations of the superfluid. Moreover, it is one of the most clearly measured polaron'' effects.