Fr Gianfranco Formenton in the Umbrian hamlet of San Martino in Trignano has started rewarded attendees with wine and crisps after services.
Writing on his Facebook page, he said: "Air conditioning... and, for the possessors of a 'mass card', aperitif prosecco from Conegliano Veneto for grown-ups and chips for the kids". Temperatures in the region are expected to reach 28 degrees Celsius this weekend.
The idea received a mixed reaction on the social media website, with one user saying: "I hope our mayor will send you a crate of prosecco for all the free publicity. Applause".
Another comment referenced Jesus driving out the money changers from the temple in Matthew 20. It called for the removal of "the merchants from the temple".
Fr Formenton told the Il Messagero newspaper the idea was "born as a game, thought up with the youth members of the parish and mainly targeted towards them.
"Every Sunday, at the end of mass, I put a stamp on the card, to certify attendance. It's just a game but it helps to remind everybody that faith is a commitment and, as such, it does not go on holiday."