In this manuscript, the authors use an experimental approach to determine how temperature affects population carrying capacity. As predicted by metabolic scaling theory, carrying capacity decreases with higher temperatures because individuals use more resources. However, carrying capacity did not scale as a simple function of the activation energy of metabolism, because of a concomitant decrease in body size due to temperature increase, which somewhat reduced resource requirements per individual.
The authors do an excellent job of showing that there is a gap in our collective knowledge about how temperatures impact carrying capacities of populations. This then motivates their chosen experimental design in which temperatures of mesocosms containing a phytoplankton species were manipulated and the resulting photosynthesis and respiration rates were measured. They also calculated expected carrying capacities based on several theoretical equations, which were explained very clearly.  
We have two suggestions for how this manuscript could be improved. First, the abstract mentions that the results of this work could have implications for global change scenarios and the final sentence mentions the impacts of the results on various ecological levels. Expanding on these possible implications in the discussion would strengthen the paper and provide potential next steps. For example:
Second, some of the experimental temperatures seemed to surpass the thermal optimum for the study species. It might be useful to present these results in a supplement, including the non-linear activation energy trend, photosynthesis rates, and body sizes for these temperatures. If global temperatures increase above species' thermal optima, these data are beneficial for understanding species responses.
The following are minor concerns about the manuscript:
Overall, we greatly enjoyed reading the paper and think it makes substantial contributions to the applications of metabolic scaling theory to population ecology. We would have been happy to receive this work as reviewers and hope it sees publication soon in an appropriate journal.