Exercising in the heat will damage your fetus.
Specific to summertime, preggos often hear this silly, parroted myth. Sources from WebMD to Babycenter pick up the thread, repeating this woman-negative, anti-scientific blather. Addionally, ACOG has recommended that women not exercise in the heat - citing insufficient evidence. Their issue with evidence isn't the lack of its existence but rather their use of twenty-five year old papers.
In order to potentially harm the fetus a mother's body temperature must exceed 102F - and I dare you to try and exercise hard enough to induce that kind of fever. The idea that exercise could raise the mother's body temperature to a level that may harm her child is untrue:
As I've discovered in the rest of my research on current pregnant athletic mythology, the myth is not only false, it couldn't be farther from the alchemic truth of the pregnant body's capabilities.
Wait a tick... how the heck does that work given we've all been told that a pregnant woman will overheat more quickly? As it turns out, the same pregnant physiology that makes pregnancy function like blood doping AND the way heat training increases heat and cold tolerance (increase in plasma volume) also allows the pregnant body to more-efficiently dispel heat during exercise. Pretty neat!
So, next time the 100s plant themselves in your town and you want to take your round, strong, pregnant ass out for a run or ride hydrate up, wear your tiniest shorts, and hit the trails - fear-free.