Controlling microalgae outdoor cultures is a growing challenge as these organisms could be used at the industrial scale to produce biofuels. In this context, understanding how temperature affects microalgae is a major field. Because of their high division rate, microalgae rapidly adapt to their environment through a process of selection -mutation so that it is not possible to neglect the evolution part. We present here a simple Monod-like model to account for temperature effect on microalgae. We then use it in an evolutionary perspective thanks to the Adaptive Dynamics theory to understand how temperature drives evolution. We analyze the model for a constant temperature, showing that the optimal temperature trait tends to equal the environment temperature. We then study the case where the temperature is periodically fluctuating, and we find a stable equilibrium. Finally, we simulate the model to show that evolutionary branching in two distinct morphs can occur under this condition, which could be a first step to find a criterion for strain selection.