Depends on how you breed them or the strain of silkworm you are working with. There are some hybrid silkworms that are stronger at resisting diseases/bacteria and eventually death than the regular white or zebra.
But most do better with an incubator, through their young stages. I usually set it at 78-80 degrees. It's through the first three stages if I remember correctly, about a week that they need the incubator. Mulberry is always the best food to use with them compared to the chow, because it molds less but it is also harder to get unless you have one in your back yard.
I keep my silks in small rubbermaid tubs, with crafting mesh on the bottom so they can be suspended above the feces they produce. All you have to do is feed them once they are passed the incubator stage and they will spin cocoons, usually they do best with something to spin their cocoon against. I use paper towel rolls, cut down. After about... I think 24-48 hours the cocoon can be moved. Before then it's too fragile to move.
After that I move all the cocoons to a larger rubbermaid container for the moths to come out and mate. Remember both rubbermaids have holes cut in the top with mesh hot glued over it. I don't mess with the moths at all. Just let them mate and sometimes feed them off when they get to the end of their life span. I feed them to my chameleon though. I always have papertowel down underneath the moths, so that when the females lay their eggs they lay it on the paper towel.
After they lay eggs, I let them turn grey (means they are fertile) and put them in the fridge for diapause until they are ready to use. I put them in a sandwhich baggie and cut out squares around the egg batches so it's not as cumbersome.
Hope this helps a bit.