Like most novels written in early nineteenth century England, there is no explicit sex here. It's all very restrained, Masterpiece Theater fare, which is appropriate. In fact, the heroine of this book is practically asexual. She even gets offended when Mary observes how attractive Edmund is.
At any rate, any sex in Mansfield Park is left largely to the imagination. It's mostly just implied. Comments that characters makes about the good looks or attractiveness of other characters signals sexual attraction, which no one could really come out and just say during this period. That said, this novel contains some scandal. Maria and Henry flirt outrageously while Maria is engaged to another man, and Maria even leaves her husband for Henry, which was scandalous on a practically apocalyptic level for this period. So the steaminess is largely restricted to scandal, and we never even get a happy love scene between Fanny and Edmund.