The recent experiments on fast (microsecond) pulse heating of graphite suggest the existence of sharp maximum (6500 K at 1-2 GPa) on its melting curve. To check the validity of these findings, we propose to investigate the accumulation of extended in-plane defects in graphene. Such defects would contribute to thermodynamic properties of graphene and impose the upper limit on its melting temperature. We propose a type of extended defect of graphene, consisting of pentagonal and heptagonal rings with record low formation energy, whose accumulation leads to the loss of shear rigidity of graphene at temperatures above 6400 K, thus setting the upper limit on its melting temperature. We found that this model satisfactorily explains the increase of specific heat observed in the premelting region of graphite in slow (millisecond) pulse heating experiments. However, in fast (microsecond) pulse heating experiments such an increase of specific heat was not observed, which is a strong indication of overheating that takes place in these experiments.