In this work we present the design and thermal modeling of a cold finger open cycle cryostat that operates with liquid nitrogen, intended to be implemented into the Mössbauer spectrometer available at the Universidad EAFIT of Medellín, Colombia, with the purpose of obtaining a low cost and good performance system for the acquisition of low temperature Mössbauer spectra. Initially, we propose a design that meets the requirements of the spectrometer, afterward, based on the initial design, we develop the calculations of heat flow into the system. The results of the thermal model allowed us to define the dimensions of the vessels, as well as calculate the evaporation time of a given column of liquid nitrogen in the cryogenic vessel. Finally, some progresses in the construction of the physical prototype are presented.