Assuming it has a thread on the inner part...
I think that's a type of ring nut.
The two slots engage with what amounts to a two-pronged screwdriver and it's undone like a screw.
Or, assuming those two large slots are a result of your sawing and wouldn't normally be there - it's a captive nut.
Or, if it's not threaded then some sort of collet.
What purpose does it serve in the thermostat - was there something passing through it?
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Giraffe: a ruminant with a view.