I always keep Vegemite in the fridge because I have lived in the hot tropics of Queensland. We love our Vegemite but if we didn't eat it fast enough when it was stored in the cupboard it developed a mould across the surface. I threw two bottles out before I learned that it shouldn't be stored in...
This would work well if the outside air is cooler than inside the house. This would have been a ridiculously stupid idea in Q'ld over the last few days when it has been 38˚ outside and 28 inside my house!