We integrated a TES X-ray spectrometer with a charged kaon beam line at J-PARC to perform X-ray spectroscopy of kaonic helium atoms. Limited beam intensity and a broad beam spot size made it crucial to increase the detector acceptance angle as much as possible, requiring significant development. To this end, our TES system shared the same vacuum with a cryogenic system of the liquid helium experimental target. We also specially developed a target cell for liquid helium and a thinned aperture array on top of the TES detector. Additionally, thermal and magnetic shields and infrared filters were optimized in terms of a larger acceptance angle and energy resolution of the detector. The scientific campaign was performed in June, 2018, where the whole system was stably operated for almost one month.