Within the spectrum of radio waves, the Ku band (12 - 18 GHz ) stands out for the wide range of instruments available and for its relative ease of acquisition, given that satellite television operates in this band. This situation offers a great opportunity for the development of radio astronomy in countries with unfavorable climatic conditions for optical astronomy, since this band is only affected by dense masses of water vapor. In this article we present a methodology for the calibration of the receiver system of compact Ku-band radio telescopes, and its application in the determination of the brightness temperature of the Moon. Our methodology involves modeling the influence of the atmosphere of the Earth on the response of the radioreceptor, which minimizes the error in the calculation of the brightness temperature of the observed object. We applied the proposed methodology in the monitoring of the Lunar cycle using the Ku-band radio telescope of the Observatorio Astronomico of Universidad Tecnológica de Pereira, Colombia (OAUTP). After observing during May, June, and July of 2021, we obtained an average temperature of 213.15 K, with maximum and minimum values of 275.55 K and 150.75 K, respectively. In addition, we evidenced a delay of 5.75 days between the phase in which the maximum temperature is presented and the phase of the full Moon, which is consistent with the frequency of observation. The results show that our methodology is useful to optimize the calibration of compact Ku-band radio telescopes, and expand the potential of this type of instrument for the scientific study of radio sources other than the Sun, in this case the Moon.