Turn it on ahead of time. I turn all my stuff on when I sit at my workbench even if I don't expect to use it. That way it is warmed up and ready. And just be more patient...
And no, that wouldn't help. Heating it to a constant temperature and keeping it there may, though, hence heated crystals and references. But heating and cooling just wastes time with no benefit - the temperatures still have to equalize when you remove the heat, just in the other direction now.
I don't think you are correct. Consider this, you are heating a glass of water at 5 degrees C using a lightbulb. You know that eventually the glass is going to reach thermal equilibrium at 30 degrees Celsius (from previous experiments). So you instead pour in water at 35 degrees Celsius, and let it cool down. I believe the water would cool down faster then it would heat up no?
Or, you heat up the water to 28 degrees C using a big heater and let the light bulb do the rest.
Is my understanding of thermodynamics wrong?
One can simply inspect a PCB with a thermal imaging camera after it has been on for several hours, determine what areas are what temperature and litter around preheating lightbulbs or some such in those areas.
If it allows more accurate measurements on seldom used equipment why not? What if you just wanna take a quick measurement thats accurate?

Maybe this is not useful for cal-labs (which are businesses in the business lol) but lower end equipment, like my function generator, which needs to run for 2 hours prior to stabilizing.
WHy not, its no more ridiculous then a soft-on power switch or booting your computer with a solid state drive (to save 30 seconds)
Some of us home users have higher end equipment which we do not want to leave on all the time.
how is it handled in your workplace?