  Cluster perturbation theory is applied to the two-dimensional Hubbard
$t-t'-t''-U$ model to obtain doping and temperature dependent electronic
spectral function with $4 \times 4$ and 12-site clusters. It is shown that
evolution of the pseudogap and electronic dispersion with doping and
temperature is similar and in both cases it is significantly influenced by
spin-spin short-range correlations. When short-range magnetic order is weakened
by doping or temperature and Hubbard-I like electronic dispersion becomes more
pronounced, the Fermi arc turns into large Fermi surface and the pseudogap
closes. It is demonstrated how static spin correlations impact the overall
dispersion's shape and how accounting for dynamic contributions leads to
momentum-dependent spectral weight at the Fermi surface and broadening effects.
