A thermal management system for an on-vehicle battery includes a battery, a first thermal element, a second thermal element, a battery mounting bracket, and a vehicle body structural element. The battery mounting bracket includes a first portion attached to the vehicle body structural element, and a second portion attached to the first thermal element. The first thermal element is attached to the first end portion of the battery, and the second thermal element is attached to at least one of the second end portion, the first and second side portions, the top portion or the bottom portion of the battery. The first thermal element is composed from a first phase-change material having a first phase-change temperature and the second thermal element is composed from a second phase-change material having a second phase-change temperature, wherein the first phase-change temperature is greater than the second phase-change temperature.