Do amps sound better when left on for 30 minutes ?

Most every piece of equipment benefits from some warm up time. Generally, turning them on is OK, but it might take a little longer to warm up than if it was pumping some music through it, even if that music is playing at low volume.

How would anyone know the answer to this critical question? I guess they would have to listen and decide. I'll do that for you for $100 or you could just do it yourself for free. Let me know what you decide is the best course.

I agree with the idea that playing the equipment speeds up the warming period. Also solid state takes along time to get stable on cold startup. That's why I usually leave my solid state on 25/7. I turn my tube equipment off, but they too warm up much faster when played rather than sitting silent. Tubes also get to a stable point faster IMHO.

It's actually pretty much an industry standard to leave solid state equipment on all the time. The designers say that the "rush" from turning on and off is more detrimental to the equipment. Tube gear, of course, would burn through tubes too often, so they need the half hour or so of warm up time.

My experience is that they don't warm fully unless they are playing music. I can leave my kW500 on for hours and it still needs playing time before it performs at its best.