Each species has adapted to a specific range of temperatures, so your first task is to pick a species and determine its optimal growth conditions.

Raising the temperature has two significant effects.

Initially the increase will speed up all reactions, making the plants grow faster, but above a certain temperature (Species specific) it will start to harm them and eventually kill them.

Second, increasing temperature decreases the amount of carbon dioxide that can dissolve in the water, thus limiting the growth of the plant.

If you can culture a single-celled alga at different temperatures, you could measure the growth rate over a week. If you are more ambitious, you could repeat the experiment while saturating the medium with carbon dioxide, and compare the two results.