By adding 2 wt% multi-layer graphene oxide (MGO) to an epoxy resin, the thermal conductivity of the composite reached a maximum, 2.03 times that of the epoxy. The presence of 2 wt% MGO percolating chains leads to an unprecedentedly sharp rise in energy barrier at final curing stage, but an increased epoxy curing degree (alpha(IR)) is observed; however, this alpha(IR) difference nearly disappears after aging or thermal annealing. These results suggest that the steep concentration gradient of -OH, originated from the 2 wt% MGO percolating chains, exerts the vital driving force on the residual isolated/trapped epoxy to conquer barrier for epoxy-MGO reaction. A modified Shrinking Core Model customized for the special layered-structure of MGO sheet was proposed to understand the resistance variation during the intercalative epoxy-MGO reaction. It shows that the promoted intercalative crosslinking is highly desirable for further improving the thermal conductivity of the composite, but it meets with increased resistance. Guided by the kinetic studies, targeted optimization on the cure processing strategy was accordingly proposed to promote the intercalative crosslinking, a thermal conductivity, 2.96 times that of the epoxy, was got with only a small amount (30 degrees C) increase of the post-heating temperature.