I would. However, where I live, a comma is used in all sentences.
Like SoothingDave, I'm pretty liberal with commas too. However, in my opinion, the one in your example sentence is optional. I would expect it to be there if you needed to pause for dramatic effect:
I heard a strange squeaking noise. I checked the cupboards. I checked the drawers. I looked behind the curtains. I checked all the floorboards. Then, I saw the mouse under the bed! Eek. I ran out of the room as fast as my legs would carry me.
If there were no requirement for a dramatic pause, I probably wouldn't even start the sentence with "Then", nor would I use the comma.
I checked the cupboards, the drawers, the curtains and the floorboards and then I saw the mouse under the bed.