I understand cabin pressure will rise, but why can't the outflow valves seal the cabin completely to simply maintain the cabin pressure? Also, will cabin temperature rise or fall?
Without a means to pressurize the airplane, cabin pressure doesn't rise; it falls. Cabin altitude climbs. With most aircraft, cabin altitude limiting will drive the outflow valves closed at a certain point, typically around 11,000 cabin pressure altitude...but this doesn't buy much or do much if the packs aren't available.
The problem is that while bleed air is available, it's too hot for cabin use, and the packs are required to deliver air for use in pressurizing the cabin. Without packs or a cooling system (packs aren't used for all aircraft), it's either emergency bleed air (if the aircraft has such a feature; not all do), or a descent to a lower altitude.
At a high altitude, cabin temperature will fall if no bleed air is being admitted to the cabin. In some aircraft that utilize emergency bleed, such as the Learjet, the cabin can get very hot.
An aircraft cabin isn't a tight pressure vessel, like a balloon. It won't stay "inflated," and leaks too much to hold pressure. In some airplanes, even items such as door seals will deflate as soon as bleed air is lost, because it's bleed and internal cabin pressure that inflates, and holds the door seal...meaning that when the bleed goes away, even more leakage occurs.