At low temperatures the excitation of conduction electrons in metals gives rise to an electronic contributionC=&Ggr;˜Tto the heat capacity, and also a contribution &bgr;∝Tto the thermal expansion coefficient, whereTis the absolute temperature. The electronic Gru¨neisen parameter is&ggr;=V&bgr;B/C=(d ln&Ggr;˜/d lnV), whereVandBare the crystal volume and bulk modulus, respectively, atT=0. We have used a local pseudopotential model to calculate all the contributions to &Ggr;˜ and its volume derivative, including the electron‐phonon interactions in first‐order perturbation. The calculated &ggr; is 1.18 for Na, 1.01 for K, and 1.63 for Al, while the measured &ggr; is 1.8 for Al. The free electron model predicts &ggr;=⅔. From our calculations it appears that the Umklapp interactions of electrons with transverse phonons give important contributions to &Ggr;˜.