First, chemical reactions usually speed up with increased temperature. This means that your developer will work faster when hotter. Many developers (and I would think that Dektol would be among them) react rather regularly to increases in temperature. In other words, if you need to use warmer developer, just develop for a shorter time. The .pdf document linked to above is a good starting point. A predictable increase in activity vs. temperature was the premise behind the Zone VI compensating developing timer, which adjusted the "seconds" of the timer based on temperature; at 68°F one "second" was really one second, at higher temperatures the "seconds" were really shorter, at lower temps, longer, allowing the standard developing time to be retained. (I love my Zone VI timer and would not like to part with it!)
Second, developers do not have to be 68°F to work correctly. Especially when printing in warmer weather, it is often easier to use the warmer, ambient temperature for "standard" rather than worry about cooling everything down. While 88°F (31°C) might be at the extreme end of things, with the right developer, it should be managable. The same applies, but with more necessity for precision and testing at different temperatures, with film, generally speaking. The real problem dealing with different temperatures is that some developers/developing agents/combinations of developing agents do not react linearly/regularly to changes in temperature, i.e., they are difficult to predict and make a nice chart for. These are usually more exotic developers. Nevertheless, they will work at different temperatures. One simply needs to test them at the particular working temperature desired.
There are a number of ways to deal with determining print development time at different temperatures. The Zone VI compensating timer is one (sometimes they are available used). Another time-honored method is the factoral method. Simply note the time it takes for a middle gray tone in the print to emerge and separate from neighboring tones and multiply that by a "factor." I find average factors to be between 4 and 6 usually. Some prints need more development and a larger factor. (As an aside, prints are "completely" developed when maximum black has been reached and the developing rate has slowed significantly. There is no particular point when a print is "done," like a turkey in the oven... You need to have enough development to get the tonalities you want. Longer development with most modern papers basically just speeds up the paper, kind of like adding more exposure.) Back to the topic... The factoral method seems to function well independent of temperature. At higher temperatures, your print will emerge more quickly and developing times will be shorter, but the factors should remain the same. This allows a measure of repeatability at varying temperatures (and a kind of adjustment for changes in developer activity due to exhaustion as well).
Finally, if developing times at high temperatures are uncomfortably short, one can simply increase the dilution of the developer to lengthen the time. Since the amount of stock solution will be less, the developer will have a smaller capacity and may need to be changed more often, but the factor should remain the same.
I develop both film and paper in trays at different ambient temperatures. I rely on my compensating timer to make the adjustments for me with the film. However, I do mix the developer at 20°C and put the developer tray into a larger tray with 20°C water in order to minimize the temperature shift during processing. For papers, however, I just let all the chemicals warm up to ambient temperature, which in the summer can be in the low 80sF. I use both the factoral method described above and my compensating time. I like it that they agree most of the time...
So, go ahead and print at ambient temperature. I wouldn't worry about cooling the chemicals down unless the high temperature was causing physical damage to the prints (emulsion sloughing off, etc.). Use the factoral method and dilute developer to control time and have fun.
Best,
Doremus Scudder
www.DoremusScudder.com