Commercial exploitation of geothermal resources requires the disposal of large volumes of cooled brine in an environmentally acceptable way. Reinjection of cooled (i.e. spent) geothermal water has become a standard reservoir management strategy. Since injected fluids are typically much colder than the reservoir rock, this strategy results in the cooling of the region around the injection wells. Injected cool water may not have sufficient residence time in the reservoir to receive enough heat from surrounding hotter rock, resulting in temperature decrease at producing wells. Usually, the energy transport in geothermal reservoirs is calculated by use of sophisticated numerical simulators. In this paper we present analytical solution of simplified model of mass and heat transfer in fractured porous medium in one dimension, assuming constant rock temperature and neglecting small-scale effect connected with dispersion and heat conduction. The solution presented in this paper is applicable if thermal capacity of rock is high but the specific area is not sufficient for instant thermal equilibrium. This approach allows for better understanding the relation between fluid movement along the fractures and heat transfer between the rock matrix and fluid. Simple numerical experiments reported in the paper have shown the importance of specific surface area of naturally fractured rock, which influences the rate of exchange of heat between the fractures and the rock matrix.