Hello, Ana4316, and welcome to the Grammar Exchange.
I've been doing some research because, like you, it sometimes seemed to me that inferential (not temporal) "then" did take a comma after it, and other times I felt the comma could be done away with, so I had decided on principle that it was optional.
I have found this material according to which, when used for enumeration or chronological sequence, no comma is used:
Sequence words include first, next, then, after that, finally.
First, I get dressed.
Then I eat breakfast.
Next, I read the newspaper.
After that, I make my lunch.
Finally, I go to school.
You can use a comma after the sequence words first, after that, next, and finally. However, you cannot use a comma after then.
First, I get up.
Next, I brush my teeth.
After that, I take a shower.
Finally, I get dressed.
Then we talk about the story.
My impression is that inferential then is more likely to take a comma after it because the pause that follows reinforces the process whereby the person reaches a conclusion after some reflection.
Please note, however, that there will be no comma if "then" reinforces the result in a conditional sentence, as in this example I found on the Internet:
If the killing was with intent to kill, and was deliberate and premeditated, then it was murder in the first degree. If it was with intent to kill, but without deliberation and premeditation, then it was murder in the second degree.