Steve Jobs demanded that the machine would be quiet and made from one piece (no holes or moving parts). This resulted in a lot of heat in the heavy cast aluminum case.

Another reason was that the Apple III is introduced to the public when there were only 3 prototypes in the world, all still wire-wrapped.

The first model had huge heat problems. There was a 100% failure rate. The advice even stated to lift the machine a few inches and drop it in order to reseat the ICs in their sockets, which gotten out because of a warped main board (because of the heat). Apple released an updated machine with ventilation holes and a smaller power supply.

Between 65,000 and 75,000 units are sold, including the first 14,000 which are recalled to fix the heating problem.
In April 1984 the production of the Apple III-line stopped. Only 4 months after the release of the Apple III+.