The critical temperature of thin Fe layers on Ir(100) is measured through
M\"o{\ss}bauer spectroscopy as a function of the layer thickness. From a
phenomenological finite-size scaling analysis, we find an effective shift
exponent lambda = 3.15 +/- 0.15, which is twice as large as the value expected
from the conventional finite-size scaling prediction lambda=1/nu, where nu is
the correlation length critical exponent. Taking corrections to finite-size
scaling into account, we derive the effective shift exponent
lambda=(1+2\Delta_1)/nu, where Delta_1 describes the leading corrections to
scaling. For the 3D Heisenberg universality class, this leads to lambda = 3.0
+/- 0.1, in agreement with the experimental data. Earlier data by Ambrose and
Chien on the effective shift exponent in CoO films are also explained.Comment: Latex, 4 pages, with 2 figures, to appear in Phys. Rev. Lett