Can I just check whether you mean new compost that you've bought, new compost that you've made in a compost bin, or used compost from old bags / pots?
My compost bin is outside and I see no reason for putting it indoors. I keep my new bags of compost in a shed so that they won't get stolen.
I wouldn't keep seedlings in the shed unless the light is sufficient there - generally it won't be enough unless it has a full bank of windows along one side. Your seedlings will get long and leggy as they draw towards the light source.
What problems do you have in the shed, which you think the sulphur candle will solve?