We study the hot charge carrier relaxation process in weakly confined hybrid lead iodide perovskite colloidal nanostructures, FAPbI$_3$ (FA = formaminidium), using femtosecond transient absorption (TA). We compare the conventional analysis method based on the extraction of the carrier temperature (Tc) by fitting the high-energy tail of the band-edge bleach with a global analysis method modeling the continuous evolution of the spectral lineshape in time using a simple sequential kinetic model. This practical approach results in a more accurate way to determine the charge carrier relaxation dynamics. At high excitation fluence (density of charge carriers above 10$^{18}$ cm$^{−3}$), the cooling time increases up to almost 1 ps in thick nanoplates (NPs) and cubic nanocrystals (NCs), indicating the hot phonon bottleneck effect. Furthermore, Auger heating resulting from the multi-charge carrier recombination process slows down the relaxation even further to tens and hundreds of picoseconds. These two processes could only be well disentangled by analyzing simultaneously the spectral lineshape and amplitude evolution.