Same here; I bought a used DeLonghi (10€!) and it's on par with a random espresso from a coffeeshop. It also doesn't take anything close to 20m to warm up, though I suppose that may be easier in Europe vs the US.
I think it takes 2-3 minutes to warm up. It's ready before I have my espresso packed. I know the instructions say to run the water a bit before brewing to clean the pipes of any colder water.
Great point on cup temp! That makes a huge difference if you want your coffee to stay warm.
Ideally you want everything the coffee touches to be at the proper temp - included th portafilter and cups.