Airguitar
The rigors a valve (or "Tube" if you're American) goes through during its life in a guitar amp are actually a lot higher and more significant than picking the ap up and moving it while it's still hot.
When the tube is at its normal operating temperature, cabinet vibration from playing subjects the tube to repetitive shock. These are actually more severe than moving the amp because they occur thousands of times a second whilst the heater is at its hottest, especially at gigging volumes.
For many years after the advent of the Transistor, Military and Aviation equipment continued to use Tubes in their critical communications equipment primarily because of its resistance to EMP, in case of nuclear warfare, but also because of it's reliability at high temperatures.
Tube wear is a known phenomenon due to the reason explained above. Even this takes a long time and it is not exacerbated by handling whilst still hot.
However, If Johnny B Goode tells you to leave his amp alone, then just leave it alone. Be cool and let him and his amp cool down. Friends!!
The best reason to move the amp around carefully is simply because you paid a lot of money for it and need it to continue functioning in the decades to come, and this is just as valid for a transistor amp.
