Skyrmions hold great promise for low-energy consumption and stable high-density information storage, and stabilization of the skyrmion lattice (SkX) phase at or above room temperature is greatly desired for practical use. The topological Hall effect can be used to identify candidate systems above room temperature, a challenging regime for direct observation by Lorentz electron microscopy. Atomically ordered FeGe thin films are grown epitaxially on Ge(111) substrates with ∼4% tensile strain. Magnetic characterization reveals enhancement of the Curie temperature to 350 K due to strain, well above the bulk value of 278 K. A strong topological Hall effect was observed between 10 and 330 K, with a significant increase in magnitude observed at 330 K. The increase in magnitude occurs just below the Curie temperature, similar to the onset of the SkX phase in bulk FeGe. The results suggest that strained FeGe films may host a SkX phase above room temperature when significant tensile strain is applied.