I have a small vacation home whose only heat source is a gas stove. It does a great job at heating the entire house when I'm there. But when I'm not there (for weeks at a time), what's the best way to keep the house minimally heated to avoid mold and mildew?

Do not use a unvented gas stove to heat with at any time. You are placing a dangerous level of CO in to your environment and the CO can kill you.

There are many ways to keep your vacation home above freezing. In mine I use a propane furnace designed for that purpose. It is set at 45 degrees all winter when I am not there. When I am there it provides safe heat for myself and family.

Read about CO here

Carbon Monoxide | Basic Information | Indoor Air Quality | Air | US EPA