To better predict how populations and communities respond to climatic temperature variation, it is necessary to understand how the shape of the response of fitness-related traits to temperature evolves (the thermal performance curve). Currently, there is disagreement about the extent to which the evolution of thermal performance curves is constrained. One school of thought has argued for the prevalence of thermodynamic constraints through enzyme kinetics, whereas another argues that adaptation can - at least partly - overcome such constraints. To shed further light on this debate, we perform a phylogenetic meta-analysis of the thermal performance curve of growth rate of phytoplankton - a globally important functional group -, controlling for potential environmental effects. We find that thermodynamic constraints have a minor influence on the shape of the curve. In particular, we detect a very weak increase of the maximum curve height with the temperature at which the curve peaks, suggesting a weak "hotter-is-better" constraint. Also, instead of a constant thermal sensitivity of growth across species, as might be expected from strong constraints, we detect phylogenetic signal in this as well as all other curve parameters. Our results suggest that phytoplankton thermal performance curves adapt to thermal environments largely in the absence of hard thermodynamic constraints.