Here you are , this is how I do it , start feeding as soon as they start hatching .
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If you have access to fresh mulberry leaves , these are your best food for baby silkworms for the first 2 - 3 weeks at which time you can swap over to chow if leaves are in short supply.
Place the petri-dish into a 600ml food tub , no lid on the petri-dish and place a smaller sized tender mulberry leaf next to it, the worms will crawl out to feed on the leaf and skeletonize it over the next 4-7 days.
If you see any sign of white or yellow fuzzy mould remove it immediately - the mould will kill the worms very fast.
I put a lid on the tub to make it air tight (keeps the worms in, helps maintain a stable microclimate, watch for condensation (I wipe it away to avoid mould formation), and it helps keep the micro-predators (ants, spider, roaches, etc out)).
No extra heat, everything happens on the coffee table at room temperature. Cleaniness is the key to success with raising and breeding silkworms.