Cracked my Coolant tank thermostat - Questions

[Meestahbig]

Hi - I removed my coolant expansion tank tonight, when I pulled it out, I think I might have cracked the thermostat. at first I thought this was a disaster and the remaining tstat piece was part of the part below 9that would be a bigger pain to replace), now I see that the tstat should pull out and I can push a new one in.

My questions, for understanding and urgency - what if the tstat is not in there. does this then not circulate coolant to the engine car, thereby causing the car to take longer to heat up? or is it the opposite, always circulating to the engine core... Or something else?

Hopefully the dealership has the part and I will get it tomorrow (I can use public transport)... but just in case. My luck, the tank split right before Easter when i need to drive... womp.