While this question is quite broad and mainly focused on the person there are some broad parameters that can be applied. Most of all does your body "Automatically" slow you down when it gets hot or you are low on water. (Wouldn't this be defined as dehydrated?) The answer would be that you mind will slow you down because you are uncomfortable far sooner than your body will shut down. Of course your heart rate will rise as the blood volume decreases. So there is a point in which you will stop. But your question is what is that point and what is the measurement of dehydration that will cause this.
Lets look at an edge case: Scott Jurek.
Scott was put in a heat chamber
In the end, Ruby said, the runner cracked as temperatures reached 135
degrees. The lab shut the experiment down for safety reasons, just
before the fuse tripped. The equipment wasn’t rated to go that high,
Ruby said, and neither was Jurek.
“He had to lower his pace and yet his heart rate kept driving up,”
Ruby said, adding that Jurek’s core temperature had climbed to 104
degrees. “That’s about the limit we allow people to get in our
chamber.”
http://missoulian.com/news/local/ultrarunner-undergoes-tv-freak-of-nature-test-on-um-campus/article_1d0cbac6-5e21-11e3-a270-001a4bcf887a.html
Most marathons will cancel the race if the heat index is above a certain level, but still the question remains does this exist? The answer is yes. What is the math? The answer is it is dependant on the individual.
I run with large group of runners every Saturday morning. (About 100-200 people) There are runners that will complete 20 miles in a little more than 2 hours and runnings that complete the 20 miles in 4 hours. All at the same temps. All in a heat index above 85-90f. Every person is different and how much they train and how much acclimation they have had makes a difference. I don't think there is any math that will calculate the exact point in which you can't go further.
In the Book "RUN: The Mind-Body Method of Running by Feel" a study was done on a group of Rugby players where they were asked to exert themselves until they had to stop. They measured the wattage they could produce. After they could go no further they were asked to go as hard as they could one more time. They were able to exceed the previous attempt. They cycled to a point of failure at 242 watts, but the second attempt they produced 731 watts for 5 seconds immediately after.
https://books.google.com/books?id=WfY5CgAAQBAJ&pg=PT29&lpg=PT29&dq=matt+fitzgerald+rugby+player+wattage&source=bl&ots=fgWkMoz4po&sig=7uiP8Oa6eFxzmrSXJVwDUu9nvoU&hl=en&sa=X&ved=0CB4Q6AEwAGoVChMI05HqodzvxwIVjJUNCh1sSA_J#v=onepage&q=matt%20fitzgerald%20rugby%20player%20wattage&f=false
The point is that your mind will tell you to quit far before you are physically not able to go on.
