Thermal and state-of-charge (SOC) imbalances are well known to cause nonuniform aging in batteries. This paper presents the electrothermal control of a multilevel converter-based modular battery to address this issue. The modular battery provides a large redundancy in synthesizing terminal voltage, which gives extra degrees of freedom in control on cell level. There are multiple tightly coupled control objectives including the simultaneous thermal and SOC balancing as well as battery terminal voltage control. The main purpose of this paper is to devise an electrothermal control scheme for cases where full future driving information is not accessible. The control scheme is based on decomposition of controller into two orthogonal components, one for voltage control and the other for balancing control. This problem decomposition enables the application of constrained linear quadratic model predictive control scheme to solve the balancing problem elegantly. The control scheme is thoroughly evaluated through simulations of a four cell modular battery. The results show that a rather short prediction horizon is sufficient to achieve robust control performance.