First off, congrats on the new addition!
I always start them off where they are going to stay. My lot are in the kitchen so when they first arrive they sleep in the kitchen. The blanket over the crate is a good idea because they have less distractions and settle well (plus it gives them the " snuggley in a safe place" feeling). I have found the best way to make this work and to keep them out of the same room as you is using baby monitors so that you will hear when they are screaming to go out (sounds crazy but it works!). However, it can take a lot of willpower not to come instantly when they cry at the very start of the night - it's very like "controlled crying" in babies, let them scream their lungs out for a while. Usually they get tired and go to sleep. It can be terrible for you at the other end of the monitor though, but persistence pays off. After a few nights they will settle in no time! Same situation when you get up to let them go to the toilet, they will eventually get tired and go back to sleep.
When they are first put into a crate for the long haul at night they can get a bit stressed so other intros to the crate are a good idea - feed them in it, give them something to play with in it etc. so that they associate it with good things. The heat pad and lots of soft stuff are great ideas, nice a cosy.
Hope nights just keep getting better for you - Good luck!