In this study, the thermal expansion behaviour of equiatomic alloys in the Mo–Nb–Ta–Ti–W system is studied to provide a predictive method to assess the behaviour of this and other high entropy alloy systems. The simulations used are based on first principles density functional perturbation theory and the quasi-harmonic approximation. Calculations have been used to predict the stability and phonon properties of increasingly complex alloys in the Mo–Nb–Ta–Ti–W system and their thermal expansion coefficients have been predicted. These are benchmarked against rule-of-mixtures predictions and experimental observations, where available. We have shown that atomic-scale modelling techniques can be used to reliably predict the thermal expansion of a range of body-centred cubic high entropy alloys and concentrated solid solutions.