We study a quantum Einstein refrigerator in which a two-level quantum system is considered as a working material and a blackbody as a reservoir. We assume that the heat transfer occurs between the system and the reservoir through absorption and emission of photons, and the particles in the two-level system follow the Bose-Einstein distribution. With all these considerations, we examine the optimal performance of the refrigerator in a high-temperature regime under the ecological function, which balances useful cooling power and the lost cooling power of the refrigerator. In our study, we discuss two cases, large contact time and short contact time limits, and find the coefficient of performance at maximum ecological function. We further derive lower and upper bounds formulation of the corresponding coefficient of performance for the two mentioned cases. We analyze that for large and short contact time limits, the optimal value of the coefficient of performance is different only when the frequencies associated with the heating and cooling stages are equal.