Rhenium is a practically important alloying element for tungsten, and in particular W-Re is used in various high-temperature applications. Regarding the thermodynamic properties, Re alloying shows an unusual, nonlinear behavior in different aspects: Firstly, small Re additions decrease the coefficient of thermal expansion (CTE), while larger Re contents lead to a higher CTE compared to pure W; secondly, Re addition always increases the bulk modulus even if the CTE is increasing at the same time, which is usually a signature of weaker bonding. Using ab-initio calculations based on density-functional theory and the virtual crystal approximation, we investigate the reason for these phenomena. We determine the influence of alloying on the elastic properties, lattice dynamics and CTE, and relate them to each other using the quasi-harmonic approximation and the Debye-Grüneisen model. We analyze how changes in elasticity and changes in the phonon band structure, respectively, influence the thermal expansion. We show that changes in elasticity alone are not able to capture the impact of Re addition on the CTE of W-Re. Instead, we show that particular features of the phonon band structure at the Brillouin zone boundary are essential to understand the origin of the anomalous thermodynamic behavior of W-Re.