The maximum size supported is usually just the maximum that they tested with when the device first came out (or was revised). There are some definate size limitations such as 48 bit LBA support, but those days (hopefully) are long gone and won't be back for a good while. Older external enclosures may have the 48 bit LBA limitation, thus having a maximum size of 137GB. Indeed BITD I had a dual drive Firewire enclosure that had this limitation. Also, if the operating system of the computer you hook it up to doesn't support a larger size, then you'll get data errors. However, if you're running at least Windows XP with any service pack installed and you're buying a new enclosure, I'd think you would be in good shape.
Regarding temperatures, all else being equal, a higher platter count means higher temperatures. However, some drives just put out less heat than others. This means a 1TB 7200.11 Seagate with 4 platters would put out more heat than a 750GB 7200.11 Seagate with 3 platters, but probably the same as a 750GB 7200.10 Seagate with 4 platters. However, comparing across brands (and sometimes across different lines of the same brand) may yield differing results.
If the drive is to be used only occasionally, then I think temperatures wouldn't matter much. However, if there is going to be almost continuous access to the drive, then you will definately want an enclosure that uses forced (fan) cooling. No matter what the manufacturers say, I have yet to see an external enclosure that did a good job in transferring hard drive heat to the exterior of the case regardless of the exterior material. I had an aluminum enclosure that was advertised as cool running, but have had hard drives lock up in it because of overheating after copying many tens of gigabytes worth of data over in one pass. With fan cooled devices, look for ones that use low profile 60mm or 80mm fans. The ones that use 40mm fans tend to either not cool as well, or be noisy.