A quantum electric current standard is the last missing piece of the quantum metrology triangle. A suitable candidate for realizing this quantum current standard is a single-electron pumping device based on a superconductor/insulator/normal metal/insulator/superconductor (SINIS) turnstile. Here, we show the temperature dependence of the single-electron pumped current of a SINIS turnstile. As the operating temperatures are increased, the current plateaus of the single-electron pumping tilt because of increased back tunneling, which originates from the thermal broadening of energy levels in the normal metal island of the SINIS turnstile. Hence, we find that to use a SINIS turnstile for the current standard at more than 300 mK, it is necessary to increase the superconducting energy gaps of the lead material and the charging energy of the island.