Here is our practice.
The cheese should always be pretty well knit after the first pressing, which takes only 5 minutes for our hard cheeses. Any longer and the curd will pull on the cloth, ruining your knit.
It is still very soft and pliable now, and full of wrinkles, but totally knit together.
The next 2 or 3 pressings, still covered, should help to form a smooth rind. After it has been covered for not more than 2 hours (Sailors 90 minute number is good, we would have it covered for about 35 or 75 minutes >5+10+20+40<) it should be pressed at room temperature, or even under.
Theses first warm pressings were aimed to knit the curd and create a good surface for the cheese (after this time, no knitting will happen). After this, the final, longer pressings aim to expel whey and remove any interior voids. This is why we press our cheeses for so long (The cheese may be in the press at 11:00 or 11:30 one morning and come out at around 6:00 the following morning)
So the slow, cool press gives you a cheese with a solid interior. This is necessary if you are making a cheese with eyes. It is also advised if you are going to age a cheese for a very long time.