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We used a thermodynamic climate model to compute the Northern Hemisphere temperature anomaly for the period 1980-2500. We obtained temperature anomalies for the ocean, the combined ocean-land area and the land. Two IPCC et al. (2007) CO2 concentration scenarios were considered, the high RCP8.5 and the low RCP4.5, we also included two estimates of the Total Solar Irradiance (TSI). We found that in the RCP8.5 scenario the effect of the TSI is to prevent the temperature for having a runaway behavior after the year 2240, that otherwise it would have due to the high CO2 emission; it is the TSI that makes the temperature anomalies to have an inflection and start decreasing. For the RCP4.5 scenario, without the solar effect, the temperature anomaly after 2075 presents an inflection and becomes constant after the year 2120, but the temperature anomaly has a clear decreasing trend when including the TSI. The TSI presents three future secular minima in the studied period. They introduce only perturbations on the general decreasing trend. The land presents the largest temperature anomalies as well as the most prominent changes, followed by the land-ocean and the ocean. We concluded that the TSI has a fundamental role in the temperature behavior over the long-term.