In short, if you feel dizzy, light headed or unwell in any other way. Or if you simply don't enjoy it. I love hot weather, and here l am on holiday on the coast of Croatia where the temperature simply refuses to dip below 35c on average. There is a hot southernly wind to add to the fun. Humidity as high as it can be. I simply cannot find the gap or a route where I could do a routine 5K without getting drenched in sweat even when walking (that's coming from a slim, usually very low sweater). I still see some guys powering through when running in the early afternoon sun, the time of day that even I wouldn't want to tackle.
Other than that, I find this weather absolutely gorgeous. A gift for madmen like me. Leaving the clouds and seeing clear skies from the plane is guaranteed to boost my morale every time.
But, and that's a big but - you only run in oppressive heat if you feel you can do it, and if you've trained to do so. Even then you've got to check with the locals first. If they don't run, you should also stay away. I made a rookie error of not doing that before and that's not bound to end up in laughter.
And for some reason I run faster in these conditions. Not sure why, but that seems to be a pattern. Anyone else out there who enjoys furnace running? Hope so. Knowing that there are more of us makes me feel less weird. Oh, and the sea temperature got to 25-26c. My idea of paradise. π