Lately, for geo-distributed data centers, a workload management approach that routes user requests to locations with cheaper and cleaner electricity has been developed to reduce energy consumption and cost. We consider two key aspects that have not been explored in this approach. First, through empirical studies, we find that the energy efficiency of cooling systems depends critically on the ambient temperature, which exhibits significant geographical diversity. Temperature diversity can be used to reduce the cooling energy overhead. Second, energy consumption comes from not only interactive workloads driven by user requests, but also delay tolerant batch workloads that run at the back-end. The elastic nature of batch workloads can be exploited to further reduce the energy cost. In this paper, we propose to make workload management temperature aware. We formulate the problem as a joint optimization of request routing for interactive workloads and capacity allocation for batch workloads. We develop a distributed algorithm based on an m-block alternating direction method of multipliers (ADMM) algorithm that extends the classical two-block algorithm. We prove the convergence and rate of convergence results under general assumptions. Through trace-driven simulations, we find that our approach consistently provides 15-20 percent cooling energy reduction, and 5-20 percent overall cost reduction over existing methods.