The present invention relates to a process for desulfurizing a cracked naphtha containing organic sulfur compounds comprising the following steps: a) feeding the cracked naphtha to a distillation column comprising a bottom reboiler; b) fractionating said cracked naphtha into a light naphtha fraction and a heavy naphtha fraction which is removed as bottoms from the distillation column; c) feeding the heavy naphtha fraction and hydrogen to a hydrodesulfurization unit containing a hydrodesulfurization catalyst to produce a desulfurized heavy naphtha effluent. The process further comprises a step of providing heat to the distillation column by an intermediate reboiler powered with a heat source having a temperature lower than that one of the bottom reboiler.