I have two cockatiels (4yo & 2.5yo) and they have never had one night fright.
My setup:
I'm lucky enough that I have a spare room I can put their sleeping cages in. I have smaller cages for just sleeping. I have two of these. and they are just sitting on top of a dresser.
I put in 1 rope perch and 1 flat perch per cage. My boy likes to change it up in the night and moves from one to the other but my girl just sleeps on the flat perch only.
I put in a small plate heater next to the flat perch. This is the one I use
I put a power strip between their cages that has a blue night light on it.
I cover the cages completely! In the summer the cover consists of double up cage covers so it's dark under there (except for the blue night light). In the winter I also cover with additional blankets to help keep in heat because I like to sleep cold.
I pop a temperature gauge between the cages so I can monitor the temps and adjust the outside covers accordingly. It never gets warmer than 79 under the covers.
I read somewhere that the key to no night frights is blocking the light. Made sense to me so that is what I do. I've had the smoke detectors go off in the middle of the night and my babies didn't get a fright. Of course, it woke them up but they were calm.