We have measured the change in the thermal conductivity of superconducting tin, indium, and lead films upon application of a magnetic field in the plane of the film. These experiments were undertaken to explore the dependence of the energy gap upon magnetic field and to determine the thermodynamic order of the field-induced transition in films. Within the range of temperatures available to us ($0.35{T}_{c}$ to $0.65{T}_{c}$) the thermal conductivity of indium and tin films increases nearly as ${H}^{2}$. In films of thickness $d\ensuremath{\geqq}2800$ \AA{} the thermal conductivity jumps at ${H}_{c}$ to the normal state value, indicating a first-order phase transition in thin films, consistent with the Ginzburg-Landau (GL) theory. If the effect of a field upon the superconducting state can be adequately represented as a change of the ${\ensuremath{\epsilon}}_{0}$ of BCS, we may use the theory of Bardeen, Rickayzen, and Tewordt to compute ${\ensuremath{\epsilon}}_{0}(H)$ from our data. At $T=0.65{T}_{c}$ we find $\frac{{\ensuremath{\epsilon}}_{0}(H)}{{\ensuremath{\epsilon}}_{0}(H=0)}={[1\ensuremath{-}{(\frac{H}{{H}_{c}})}^{2}]}^{\frac{1}{2}}$ in agreement with the GL prediction. At $T=0.35{T}_{c}$ however, $\frac{{\ensuremath{\epsilon}}_{0}(H)}{{\ensuremath{\epsilon}}_{0}(0)}=1\ensuremath{-}{(\frac{H}{{H}_{c}})}^{2}$ provides a more satisfactory fit to our data. Orientation of the field \ensuremath{\perp} and \ensuremath{\parallel} to the direction of heat flow produces the same effect on the thermal conductivity to \ifmmode\pm\else\textpm\fi{}1%. This is interesting in view of Bogoliubov's prediction of a ${\mathrm{p}}_{F}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{v}}_{\mathrm{drift}}$ term in the excitation spectrum of a current-carrying superconductor. When the field is not parallel to the surface of the film the thermodynamic transition is still sharply defined, but ${H}_{c}$ is reduced. Thin lead films gave results similar to those of indium and tin films except that at low fields the field-dependent conductivity increased more slowly than ${H}^{2}$ at low temperatures.