Why not a line plot? A line plot seems pretty fitting if you'd like to show general trends in mean and SD provided individual specie is not the focal point.
Anyway, here is an alternative, which strictly speaking is still a line plot but time is not one of the axes. It is also good for discussing individual species. x-axis is your variable 1 (I guessed that's mean), y-axis is the variable 2 (SD).
And yes, heat map maybe too much, but I think it's worth a try to show 3D kernel density if you can provide the actual data as well. Codes are taken from this thread.
Another possibility is to make three plots:
- t1 SD vs. mean, use black symbol
- t1 SD vs. mean, but this time the symbol turned to light grey; overlay t2 SD vs. mean, use black symbol. Connect each species pair with an arrow.
- t2 SD vs. mean, but this time the symbol turned to light grey; overlay t3 SD vs. mean, use symbol. Connect each species pair with an arrow.