For Bombyx ,mori ,the optimum temperature for normal growth of silkworms is between 20°C and 28°C and the desirable temperature for maximum productivity ranges from 23°C to 28°C. Temperature above 30°C directly affects the health of the worm. If the temperature is below 20°C all the physiological activities are retarded, especially in early instars; as a result, worms become too weak and susceptible to various diseases.At a humidity of 90 percent or higher, if temperature is maintained at 26°C–28°C, they can grow without being greatly affected. Like temperature, humidity also fluctuates widely not only from season to season but also within the day itself.
I guess you are talking about Mulberry silkworm, Bombyx mori. Other than temperature and RH, do not miss to maintain cleanliness; daily sterilization of the tools that you use for rearing is very important as silkworm larvae are very prone to number of diseases. Voltinism of the silkworm is also one important aspect to consider. Try to know if your silkworm is uni-, bi- or multivoltine. Depending upon voltinism, egg production and hatching methodology shall differ.