We developed a cryocooled helmet-shaped magnetoencephalographic measurement system. We determined the sources of white noise that contribute to the total white noise of this system and determined the source of cyclic noise generated by the Gifford-McMahon-Joule-Thomson cryocooler. Design modifications based on these results will reduce the white noise of our future cryocooled systems to 5 fT Hz-1/2 for cyclic noise to 1 pT.