The quantum Heisenberg hyperfilm is studied by the variational-cumulant exp
ansion method. From the analytic properties of free energy, the critical re
duced temperature theta(c)(l) can in principle be calculated to any order c
umulant expansion as a function of the number l of hyperlayers in hyperfilm
. Explicit expressions for theta(c)(l) up to the third order are given for
various lattices and spins.