“We hoped we would get some notice, but we never expected to get the attention we got,” he said. “Let’s face it, it’s in the middle of nowhere.”

A year ago, he said, he normally got two or three inquiries a day about village rentals. “Yesterday alone, I got more than 400,” he said. In the first 10 days, there were 17 bookings, including a large group from Holland.

The road to Megyer leads southwest from Budapest for two hours, through the Somlo wine district and its steep, rocky vineyards before dipping south, crossing the Marcal River and curving into the small cluster of pale cottages that is the village.

Gusztav Egly, 62, the on-site caretaker, moved between the old municipal offices and the construction site for a new sauna, a hatchet in his hand.

“In order for this to become a true holiday village, there is still work to be done,” he said, pointing to a tottering wooden fence near a chicken coop held up by wire and weeds. “That is my project for next week.”

Heat in the village comes from firewood, biomass pellets and the occasional electric heater. Propane fires the only gas-burning stove. The sole Internet connection is a weak Wi-Fi signal in the municipal offices; there is one television, and there are no landline phones.

Mr. Egly pulled open the door to the 150-year-old municipal building, strode to the reception desk and slapped the bell. Eniko Bakonyi, 52, the office manager and only other full-time employee, emerged from a chilly back room. With no guests at the moment, the buildings were all kept bracingly cold, forcing Mr. Egly and Ms. Bakonyi to wear their winter coats indoors.