  We study the effects of time-dependent substrate/film temperature in the
deposition of a mesoscopically thick film using a statistical model that
accounts for diffusion of adatoms without lateral neighbors whose coefficients
depend on an activation energy and temperature. Dynamic scaling with fixed
temperature is extended to predict conditions in which the temperature
variation significantly affects surface roughness scaling. It agrees with
computer simulation results for deposition of up to ${10}^4$ atomic layers and
maximal temperature changes of $30 K$, near or below the room temperature. If
the temperature decreases during the growth, the global roughness may have a
rapid growth, with effective exponents larger than 1/2 due to the
time-decreasing adatom mobility. The local roughness in small box size shows
typical evidence of anomalous scaling, with anomaly exponents depending on the
particular form of temperature decrease. If the temperature increases during
the growth, a non-monotonic evolution of the global roughness may be observed,
which is explained by the competition of kinetic roughening and the smoothing
effect of increasing diffusion lengths. The extension of the theoretical
approach to film deposition with other activation energy barriers shows that
similar conditions on temperature variation may lead to the same morphological
features. Equivalent results may also be observed by controlling the deposition
flux.
