The ability of Lithium-ion batteries to perform work decreases at low temperature of operation; a common strategy to improve their productivity is to warm them. In our recent works we have raised the need to study the energy-optimal warm-up of batteries. More recently, our work used battery temperature to determine if the battery has warmed up. The power capability of batteries is a more relatable and arguably useful means to terminate the warm-up process. This work builds upon its predecessors by using power capability as stopping condition, analyzes the problem and numerically solves the same. Subsequently, the relation between the minimumtime and minimum-energy warm-up problem formulations that employ temperature and power constraints to terminate warm-up are theoretically established.