For safety, you should keep yogurt warm as it can be out-competed by harmful things, I once tried using something like this:
http://smile.amazon.com/TAYAMA-YX-45A-Tayama-Vacuum-Pot/dp/B...
But I found it difficult to get a thermal pot down to the right temperature range to begin yogurt and switched to making only kefir. Kefir is less likely to lose to a contaminant at room temperature as it is a diverse cocktail.