  This paper is devoted to the study of the evolution of holographic complexity
after a local perturbation of the system at finite temperature. We calculate
the complexity using both the complexity=action(CA) and the
complexity=volume(CA) conjectures and find that the CV complexity of the total
state shows the unbounded late time linear growth. The CA computation shows
linear growth with fast saturation to a constant value. We estimate the CV and
CA complexity linear growth coefficients and show, that finite temperature
leads to violation of the Lloyd bound for CA complexity. Also it is shown that
for composite system after the local quench the state with minimal entanglement
may correspond to the maximal complexity.
