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Depends.
If your group is not comfortable with sexual/romantic content in their game, you do not roleplay it at all. It is really not necessary. You can play a catfolk just fine without worrying about heat, and there's nothing that says that catfolk picked up that particular feature from cats.
If your group is comfortable with sexual/romantic content, play the character as if she is more sexually aroused than normal. She will be flirtatious and might invite someone to her room in the inn or to share her sleeping bag if in camp. She is not likely to be indiscriminate in her affections - she is horny, but she's not one of the ladies in those Axe commercials who throw themselves mindlessly at any available man. Note that if you're assuming that catfolk experience heat she will be uninterested in sex at all other times - this is typical of species that have an estrous cycle. If you want to be subtle (and I highly recommend subtlety) then just assume that she has a more predictable cyclic pattern of "in the mood" and "not in the mood" than your average human.
Be very careful not to overdo it, especially if you are male and especially if you are male and there is a female in your gaming group. This sort of thing can easily make people uncomfortable, especially if someone feels you are using your character in a self-gratifying way.