We describe an experimental setup for conversion electron Mössbauer spectroscopy (CEMS) at low temperature. The setup is composed of a continuous flow cryostat (temperature range of 4.2-500 K), detector housing, three channel electron multipliers, and corresponding electronics. We demonstrate the capabilities of the setup with CEMS measurements performed on a sample consisting of a thin enriched 57Fe film, with a thickness of 20 nm, deposited on a silicon substrate. We also describe exchangeable adaptations (lid and sample holder) which extend the applicability of the setup to emission Mössbauer spectroscopy as well as measurements under an applied magnetic field.