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• A thermal evolution model is proposed to explain the activity of the Halmahera volcanic arc. • Our results can explain why there are magmatic gaps and volcanic arc migration during subduction and rollback. • The thermal simulation results show that a smaller subduction rate or a larger convergence rate are favorable to the occurrence of island arc magmatism. The Halmahera volcanic arc has experienced intermittent volcanic activity and location migration since the Pliocene. Two factors affect the volcanic arc magmatism. One is the dehydration depth of hornblende in the oceanic crust and serpentinite in the lithospheric mantle in the subducted slab. The other is the subducted slab and mantle wedge temperature structure, controlled by the subduction rate and plate convergence rate. Thermal simulation results show that conditions are favorable to the occurrence of island arc magmatism at a lower subduction rate with the same convergence rate, or at a higher convergence rate with the same subduction rate. The Miocene–Pliocene favored the occurrence of island arc magmatism in the high temperature region, because there was a lower subduction rate beneath the Halmahera volcanic arc. After the Middle Pliocene, there was cessation of volcanic activity and a volcanic gap, with subsidence of the mantle wedge high temperature region, increase of the partial melting depth, and decrease of the melting amount, because there was an increased subduction rate beneath the Halmahera volcanic arc and a decreased westward convergence rate of the eastern microplate fragments. In the Holocene, the Halmahera arc moved to a new location and resumed volcanic activity. It is because continuous arc–arc collision blocked the westward movement of the Halmahera volcanic arc, the relative convergence rate of the eastern microplate increased, which resulted in the formation of a high temperature region favorable to island arc magmatism. [ABSTRACT FROM AUTHOR]