Yes. Cut the flower stalk off. Give it dormancy.

That brings up a good question -- what are the criteria for deciding when to put a VFT or American Pitcher Plant into the fridge for dormancy?

First frost? First night under freezing? First week with highs down in the 50s?

I need to move mine into the fridge but I am petrified of killing it by putting it in too soon. There are no cold windowsills in my apartment, and with a Southern Idaho winter, I'm worried being outside will be too much.

When it's been outside in the cold night for a number of weeks, so the plant knows it's time to shut down. Mine went in the fridge prior to first frost, last week. I have several sarrs that will go in today actually.