A theoretical analysis of the coefficient of performance COP was undertaken to examine the efficiency characteristics of the monomethylamine–water solutions for a single-stage absorption refrigeration machine, using low generator temperatures (60–80°C), which allows the use of flat plate solar collectors. The thermodynamic analysis considers both, basic and refined cycles. The refined absorption cycle included a sensible heat recover exchanger (that is a solution heat exchanger). The thermal coefficients of performance COPh for the basis cycle and COPSHE for the refined cycle were calculated using the enthalpies at various combinations, at the operating temperatures and concentrations. The flow ratio FR has been calculated as additional optimization parameter. Due to the relative low pressure and the high coefficients of performance, the monomethylamine–water solutions present interesting properties for their application in solar absorption cycles at moderate condenser and absorber temperatures (25–35°C), with temperatures in the evaporator from −10°C to 10°C which are highly usable for food product preservation and for air conditioning in rural areas.