Just bought a laptop. Made sure I didn't type above 5 words per minute for the first couple of hours to let the processor burn in. After that I kept it down to 10 words per minute, just so the RAM and the I/O system could settle down. Now that I have been using it for 50 hours, I feel comfortable using it for web surfing, safe in the knowledge that the graphics processor is properly burnt in.
Claptrap? you bet. But no more so than the nonsense on this thread about burning in. The tolerances in a PC are hundreds of thousands of times more critical than an amp, yet the damn things work straight out of the box.
As cheeseboy points out however, temperature has a very significant effect on component performance. Critical electronic timing components are kept in temperature controlled 'ovens' to ensure that they remain stable, and 'thermal runaway', where an increase in temp causes a component to draw more current and in turn get hotter leading to ultimate failure is a well known problem.
Good designers design around thermal sensitivity, but it would not be impossible for an amp to have slightly different performance after it has reached a stable operating temperature.