There is little use in adding a thermistor to this transformer. You do not state where it would be. Most of the places I could imagine placing it would either lead to no function to pretty sparks & smoke (once).
I was thinking of adding it in series on the primary side (220V) to limit inrush current to avoid too much strain on the mains power cable, switch, fuse, etc.
The traffo is used in a bench PS like I said above. Will it be fine to ditch the thermistor?