We investigate the pseudo specific heat of SU(2) gauge theory near the
crossover point on 4(4) to 16(4) lattices. Several different methods
are used to determine the specific heat. The curious finite size depen
dence of the peak maximum is explained from the interplay of the cross
over phenomenon with the deconfinement transition occurring due to the
finite extension of the lattice. In this context we calculate the mod
ulus of the lattice average of the Polyakov loop on symmetric lattices
and compare it to predictions from a random walk model.