The linear coefficient of thermal expansions for the 4d, 5d, and the 5f transition elements is considered theoretically by means of first principles electronic structure calculations. The calcluations utilize the LMTO-method within the local density approximation (LDA) for the exchange-correlation potential, and are fully relativistic. A simplified expression for the Debye temperature is combined with the Gruneisen theory to obtain the thermal expansion. The theoretical results are in relatively good agreement with experiment. The behavior of the thermal expansion for the 4d transition metals is very similar to that for the 5d transition metals, while the 5f metals display a different variation over the series. Especially Np and Pu show a most anomalous thermal expansion, which is suggested to originate mainly from relativistic effects.