This paper deals with the analysis of global temperatures and sunspot numbers and the relationship between the two. We use techniques based on the concept of long range dependence. For the temperatures, the best specification seems to be a fractionally integrated or I(d) model with an order of integration d of about 0.46 and an estimated time trend coefficient that suggests that temperatures have increased by about 0.57 °C over the last one hundred years. However, for the sunspot numbers, a cyclical fractional model seems to be more appropriate, with a periodicity of 11 years per cycle and an order of integration of about 0.40. Thus, the two series display long memory and fractional integration. However, the fact that both series display poles in the spectrum at different frequencies implies that we fail to reject the null hypothesis of no relationship between the two variables in the long run. Moreover, assuming that the sunspots are exogenous, the results show no statistical significance of this variable on the global temperatures, which is one of the main contributions of the present work.