Psilocybin will not break down when boiled, but psilocin will. The hotter the water the better for a psilocybin extraction, but consequently you're going to lose all psilocin in the mushrooms. In some cases this can be significant. Once psilocybin is ingested it is dephosphorylated and becomes psilocin, which is responsible for the hallucinogenic effects of magic mushrooms. Your best bet is to bring the water to a boil and remove the pot from the heat source then put in the finely chopped mushrooms stirring occasionally for the next 10-15mins. By heating the water you are increasing the average kinetic energy simply to facilitate the extraction. Psilocybin is extremely water soluble so there really is no need to boil the mushrooms.
If you really want to get the most out of a mushroom trip try using a MAOI such as black currant juice. Black currant juice will prolong the trip and make it more intense. Or look into the Lemon/Lime method. You can soak mushrooms in fresh Lemon/Lime juice to help jump start the psilocybin->psilocin process which can in turn significantly increase the intensity of the trip.