Two-way ANOVA to detect difference in activity at different temperatures?

I need to answer the question of whether three species differ in their activity pattern according to soil temperature. Activity pattern is measured as the mean number of individuals observed in transects where each temperature was recorded and, hence, is not an integer. My data table looks something like:

Temp Sp1 Sp2 Sp3
20 0.10 0.00 0.00
21 0.20 0.10 0.00
24 0.35 0.26 0.00
26 0.28 0.38 0.20
27 0.17 0.45 0.30
... ... ... ...

The activity patterns are best explained by quadratic models, not linear ones. It seemed to me that it was a two-way ANOVA sort of question but after reading around, my two sources of variation (Temperature and species) aren't really equivalent to the factors I saw explained for two-way ANOVA problems (e.g. difference in weight according to diet and sex). Can someone please help me figure out what test I should use to see whether the three species have a different activity pattern according to temperature (or whether activity peaks at different temperatures between species)?