We study the ultrafast magnetization dynamics of bcc Fe and fcc Co using the recently suggested heat-conserving three-temperature model (HC3TM), together with atomistic spin- and lattice dynamics simulations. It is shown that this type of Langevin-based simulation is able to reproduce observed trends of the ultrafast magnetization dynamics of fcc Co and bcc Fe, in agreement with previous findings for fcc Ni. The simulations are performed by using parameters that to as large extent as possible are obtained from electronic structure theory. The one parameter that was not calculated in this way, was the damping term used for the lattice dynamics simulations, and here a range of parameters were investigated. It is found that this term has a large influence on the details of the magnetization dynamics. The dynamics of iron and cobalt is compared with previous results for nickel and similarities and differences in the materials' behavior are analysed following the absorption of a femtosecond laser pulse. Importantly, for all elements investigated so far with this model, we obtain a linear relationship between the value of the maximally demagnetized state and the fluence of the laser pulse, which is in agreement with experiments.