Actually the 1/3 power continuous power test is a lot harder on an amplifier than continuous full power operation.
At full power most of the heat is dumped into the load, not into the amplifier. At 1/3 power most of the heat is dumped back into the amplifier.
The old FTC test standard came about because of wildly inflated "brown box" commercial gear of the time, some advertising 1000 watts peak power with little sold state amplifier built into the furnature like coffins that only put out 10 watts or so real. The 1/3 power test was simply picked out of thin air without an understanding that it was actually near worst case operation, and not like real world use conditions at all. Many companies with quality products had to change their products. Crown, for example with their battleship like 300 amplifier moved the thermal protection breakers from the transistors themselves to far away out on the heat sinks, so they would not trip as fast. The amplifier never did have any power or heat problems, but the rules meant they had to remove protection for the user. It was a bad regulation. Bob Tucker of Dynaco did a major white paper on the subject. Even the old Dyna St-70 tube amp had to be downrated in power because of it.
Bob Carver, as I understand it, got around the rules because his little cube was designed to run with the small amp section at near full power under 1/3 power test conditions, with the high power mode essentially turned off, so a big heat sink was not required, just enough needed for the 5 minute full power end test, starting when it had not been heated up with the worse case 1/3 power preconditioning.
In recent years, I doubt if there has been any enforcement of these rules as they were pretty well understood to not be very useful.
We have never provided thermal shutdown circuits on new AVA amplifiers because we have never had a reported case of output circuit damage that was overheating related. In our vigorous 1/3 power testing here, we note that the output transistor cases always stay within the manufacturer's safe operating range, and more important yet, the thermal gradient between the output cases themselves and the very end of the heat sink fins is very small, indicating that the heat sinks are doing an excellent job of pulling the heat out of the devices and dumping it into the air. The heat sinks themselves are "striated" (many small grooves) which nearly doubles their effective size.
But in any event, don't worry if your own amplifier (whatever brand) flunks a pre-conditioning test, it is not a real world situation and likely has no good correlation to the unit's actual audio performance.
Now advertised power for car radios and multi-channel surround sound systems, well that is a different tale entirely, and subject to more thought on a quiet rainy day when I have nothing better to expand on.
Frank Van Alstine