The special bonus for praying of priest, monk and knight only refer to the chapel, and not also to the temple, right?

The Temple space says "Pray" so the bonus applies.

Shrine Adventure card also uses "Pray" and there is the Idol card from Reaper I think, which is basically Temple in Adventure card form.

Yes, but the character cards of Knight, Monk and Priest say "the die", that's why I was confused.