Everyone always asks me about how to know when too hot is too hot for the pups. I have said before, for me, it is a combination of heat + humidity + availability to water (i.e. puddles deep enough to lay down in) + shade. Sometimes if the heat is higher, BUT the humidity is lower, I will let them go with me. It really seems like the combo of the two, heat and humidity is what kicks my ass, so I know it doubly kicks theirs, since they are wearing a fur coat.
I have heard that a good rule of thumb is to add the temperature to the humidity and IF the number is 150 or greater, then the run is a NO GO. I also take into account if you are running on trail versus pavement. We do have to run over a little bit of pavement to get to the rural roads that are on our route, so I will test the pavement with my bare feet or palms to see if it is cool enough for the dogs to run on. I also try to head out very, very early in the morning, usually around 4:30 am to avoid the Kansas heat. I am a wuss when it comes to running in the heat too, so that works for both me and the dogs. If I am doing a long run and I know that at some point, we will be in the sun and the heat, I will plan to loop by the house around sunrise, so that I can drop the dogs off.
I also DO NOT run with headphones, so that I can hear my dog's foot fall and breathing patterns. I try and stop every mile or two miles, depending on how they are handling the heat for water breaks. I bring water for them and me and will bring their collapsible bowl for drinking. I use the little silicone collapsible bowls that you can get at any pet store or amazon. They come with carabiners or you can just fit them in your pockets.
Sometimes they just won't drink and I will let them have some of my water that has flavor in it due to electrolyte supplements. I have also heard you can add baby food to the water to encourage drinking. Also remember, dogs don't use fuel like we do and dogs don't have the same nutrition needs as we do as runners. They use fat for fuel versus the carbs we need, so don't give them traditional running fuel. You can cause major GI distress in your dog by giving them high carb or high sugar fuel.