Transient absorption spectra (TAS) of lead halide perovskites can provide important insights into the nature of the photoexcited state dynamics of this prototypical class of materials. Here, we perform ground and excited state molecular dynamics (MD) simulations within a restricted open shell Kohn-Sham (ROKS) approach in order to interpret the characteristic features of the TAS of CsPbBr3. Our results reveal that properties such as the finite temperature band gap, the Stokes shift, and therefore, also the TAS are strongly size-dependent. Our TAS simulations show an early positive red-shifted feature on the fs scale that can be explained by geometric relaxation in the excited state. As excited-state processes can crucially affect the electronic properties of this class of photoactive materials, our observations are an important ingredient for further optimization of lead halide based optoelectronic devices.