Disas are very forgiving. They will grow and survive hot spells of over 100 degrees F and also the occasional frost. The Summer of 2000 started off in my area with a couple of days where the temperature got to 100. Unfortunately one of those days corresponded with a day that I was away from home and in which I also had a power outage which blew my circuit breakers. I arrived home that night and discovered some of the leaves and virtually all the early flowers and flower spikes severely wilted. I sprayed everything down with water and turned on the misters for a while and by the next morning the plants and spikes looked better but most of the flowers were damaged. The high/low recording thermometer that I keep at pot level recorded a high of 118 degrees Fahrenheit. I have usually had summer temperatures in the 90's in the greenhouse but the high pressure mister has so far kept the temperatures under 100 when it has been working.
On the other side of the temperature range, Disas will survive an occasional frost and even short periods of temperatures below freezing. I have been a bit chicken about subjecting my Disas to this low a temperature because I have some other orchids housed with them. However, both the New Zealand growers and Wally Orchard who is up in Olympia Washington have had experience with frosts and even snow on the Disas and claim they come through unscathed. This doesn't mean that they can be left in sub freezing temperatures for days on end but that they can take an occasional overnight frost. If you have conditions where the tuber is frozen, you will probably loose the plant.
The root temperature is reputedly another area of concern. Since I live in an area that has some Ocean influence, Sunset designates this area as Zone 14 - moist, I always have a quite marked drop in temperature at night. This nightly temperature drop allows the Disas to recoup from any daytime temperature stress and also keeps the overall root temperature low. It is not uncommon for the summer nighttime temperature to get to the 50's. As a result, I don't usually have to worry about root temperature and don't often monitor it. For those of you who live in an area where the nighttime temperature stays high, root temperature might be a problem. While I don't have any hard scientific data, a number of South African growers carefully monitor root temperature and claim that any prolonged periods of root temperature above 70 degrees F will cause problems. This might be overcome by using unglazed ceramic pots but I don't have any personal experience.
The last area that I want to discuss is the difference between day and night temperature. Disas definitely like cool temperatures and in nature experience a wide variation between day and night temperatures. They are cooled at night and often partially shaded during the day. Ideally, they probably do best in the range from 40 to 75 degrees F. In talking to people who try to grow Disas under relatively stable conditions like a basement, unless you can get a 20 degree temperature swing between day and night, you will probably experience difficulty.