  Thin films of superconducting V$_3$Si were prepared by means of RF sputtering
from a compound V$_3$Si target at room temperature onto sapphire and
oxide-coated silicon wafers, followed by rapid thermal processing under
secondary vacuum. The superconducting properties of the films thus produced are
found to improve with annealing temperature, which is ascribed to a reduction
of defects in the polycrystalline layer. Critical temperatures ($T_\text{c}$)
up to $15.3\,$K were demonstrated after thermal processing, compared to less
than $1\,$K after deposition. The $T_\text{c}$ was found to always be lower on
the silicon wafers, by on average $1.9(3)\,$K for the annealed samples. This
difference, as well as a broadening of the superconducting transitions, is
nearly independent of the annealing conditions. In-situ XRD measurements reveal
that the silicide layer becomes strained upon heating due to a mismatch between
the thermal expansion of the substrate and that of V$_3$Si. Taking into account
the volume reduction due to crystallization, this mismatch is initially larger
on sapphire, though stress relaxation allows the silicide layer to be in a
relatively unstrained state after cooling. On oxidized silicon however, no
clear evidence of relaxation upon cooling is observed, and the V$_3$Si ends up
with an out-of-plane strain of 0.3\% at room temperature. This strain increases
as the sample is cooled down to cryogenic temperatures, though the deformation
of the polycrystalline layer is expected to be highly inhomogeneous. Taking
into account also the reported occurrence of a Martensitic transition just
above the critical temperature, this extrapolated strain distribution is found
to closely match an existing model of the strain dependence of A-15
superconducting compounds.
