Epitaxial Fe(Se,Te) thin films were prepared by pulsed laser deposition on (La0.18Sr0.82)(Al0.59Ta0.41)O3 (LSAT), CaF2-buffered LSAT and bare CaF2 substrates, which exhibit an almost identical in-plane lattice parameter. The composition of all Fe(Se,Te) films were determined to be FeSe0.7Te0.3 by energy dispersive X-ray spectroscopy, irrespective of the substrate. Albeit the lattice parameters of all templates have comparable values, the in-plane lattice parameter of the FeSe0.7Te0.3 films varies significantly. We found that the superconducting transition temperature (Tc) of FeSe0.7Te0.3 thin films is strongly correlated with their a-axis lattice parameter. The highest Tc of over 19 K was observed for the film on bare CaF2 substrate, which is related to unexpectedly large in-plane compressive strain originating mostly from the thermal expansion mismatch between the FeSe0.7Te0.3 film and the substrate.