The increase in data storage and power consumption at data-centers has made it imperative to design energy efficient Distributed Storage Systems (DSS). The energy efficiency of DSS is strongly influenced not only by the volume of data, frequency of data access and redundancy in data storage, but also by the heterogeneity exhibited by the DSS in these dimensions. To this end, we propose and analyze the energy efficiency of a heterogeneous distributed storage system in which $n$ storage servers (disks) store the data of $R$ distinct classes. Data of class $i$ is encoded using a $(n,k_{i})$ erasure code and the (random) data retrieval requests can also vary across classes. We show that the energy efficiency of such systems is closely related to the average latency and hence motivates us to study the energy efficiency via the lens of average latency. Through this connection, we show that erasure coding serves the dual purpose of reducing latency and increasing energy efficiency. We present a queuing theoretic analysis of the proposed model and establish upper and lower bounds on the average latency for each data class under various scheduling policies. Through extensive simulations, we present qualitative insights which reveal the impact of coding rate, number of servers, service distribution and number of redundant requests on the average latency and energy efficiency of the DSS.