Overheating is where you consume a lot of favour in a short time while channeling. To do this you would need to either sacrifice items at an altar or use gems to recover favour quickly. This state is normally associated with the gem draw method of recovering favour as sacrificing effectively counts as a thirty second pause in casting thus reducing the likelihood of overheating. Mind speed raises the ceiling before you overheat so if this is an issue then development of this characteristic is a must.
Most priests will either cast when their favour recovers naturally or cast after sacrificing items. In both these cases overheating is not an issue. The time a priest normally requires a lot of gems for fast favour recovery is when they are involved in PvP. This is where almost all known instances of overheating are seen. Typically it is the casting of the area of effect spells that will trigger this issue.
Once you've hit this barrier you will be unable to cast spells until the cool down effect expires. This appears to be approximately two minutes after each cast so the cool down is complete two minutes after your last cast. If you cast again before the cool down is complete then its possible to pass the threshold again immediately and have to wait again.
As a comparison think of it as a leaky bucket. The holes are the cool down mechanism but every time you cast you dump a load of water in. The more favour you used, the more water goes in. With the bucket you can only cast if the bucket is less than three quarters full. Space your casts apart enough and the bucket is always almost empty. Cram the casts together and the water cannot drain off fast enough. Get a big cast as your last one and you can pretty much fill the bucket to the brim which means you'll be waiting a while to cast again as it has to drop to only three quarters full.