Variations of temperature values for the last 20 000 years measured in the cave Dos Anas (Sierra del Rosario Cuba) are studied in comparison with the values of the hydrogen isotopes concentration obtained in the coral reef of the Barbados Island in the Caribbean region. They are compared as well with the abundance of Be10 measured in the permanent layers of ice of Central Greenland representative of the global temperature for the same period The solar activity manifestation is evidenced in the temperatures measured in a stalagmite of the cave Dos Anas when being proven that an increment of the temperatures belongs together with a decrease of the production of isotopes. This behavior is consequence of a smallest quantity in cosmic rays arriving to the Earth as result of an increment in the solar activity. The 2 000 years interval of temperature reduction observed in the curves can be interpreted like a stage of low solar activity alike it has been observed in other Sun type stars. The scale of variation of the influence in climate due to the orbital dynamics of the Earth in that interval is not significant.