It could very well be minutes...it really depends on the runner. I only have anecdotal experience with this, but it was a huge issue for myself. I've noticed that some athletes only take a marginal hit, say a couple seconds per mile, but they are able to perform the same kind of races/workouts. For example, a 10 miler at 6:00 pace might be a 10 miler at 6:10-6:15 pace, at the same effort. On the other hand, and this is where I fall, there are athletes who complete crash out and take huge performance hits on top of the marginal disadvantages. This type of athlete might go from a 10 miler at 6:00 pace to a 6 miler at 6:10-6:15 and then the last 4 miles at 6:30 pace or stop altogether.
One summer in particular I was doing weekly threshold runs of over an hour, and I was fit enough to have a good feel for pace. If I got a particularly hot or humid day, I might only make it half way before crashing and having to abandon the workout. And it really is dewpoint more than raw temperature. The body needs to cool itself. To do so, sweat is produced to cool the skin and circulation is directed to the periphery so that the blood can transfer heat. This means less blood to muscles, and more work for the heart. Many times I would feel fine at the beginning of a workout because the pace really wasn't that fast, but as I overheated, my breathing and heart rate would sky rocket instead of progressively increasing over the duration of the workout.
So to answer your question, anywhere from 10 seconds a mile (1:00) for someone who has efficient cooling to 5:00 for someone who is incredibly fit but can't operate anywhere near top form under such conditions.