Understanding the ultrafast demagnetization of transition metals requires pump-probe experiments sensitive to the time evolution of the electronic, spin, and lattice thermodynamic baths. By means of time-resolved photoelectron energy and spin-polarization measurements in the low-pump-fluence regime on iron, we disentangle the different dynamics of hot electrons and demagnetization in the subpicosecond and picosecond time range. We observe a broadening of the Fermi-Dirac distribution, following the excitation of nonthermal electrons at specific region of the iron valence band. The corresponding reduction of the spin polarization is remarkably delayed with respect to the dynamics of electronic temperature. The experimental results are corroborated with a microscopic 3-temperature model highlighting the role of thermal disorder in the quenching of the average spin magnetic moment, and indicating Elliot-Yafet type spin-flip scattering as the main mediation mechanism, with a spin-flip probability of 0.1 and a rate of energy exchange between electrons and lattice of 2.5Kfs⁻¹.