© 2014 Elsevier Inc. All rights reserved. Abstract The need for greater performance in high performance computing systems combined with rising costs of electricity to power these systems motivates the need for energy-efficient resource management. Driven by the requirements of the Extreme Scale Systems Center at Oak Ridge National Laboratory, we address the problem of scheduling dynamically-arriving tasks to machines in an oversubscribed and energy-constrained heterogeneous distributed computing environment. Our goal is to maximize total "utility" earned by the system, where the utility of a task is defined by a monotonically-decreasing function that represents the value of completing that task at different times. To address this problem, we design four energy-aware resource allocation heuristics and compare their performance to heuristics from the literature. For our given energy-constrained environment, we also design an energy filtering technique that helps some heuristics regulate their energy consumption by allowing tasks to only consume up to an estimated fair-share of energy. Extensive sensitivity analyses of the heuristics in environments with different levels of heterogeneity show that heuristics with the ability to balance both energy consumption and utility exhibit the best performance because they save energy for use by future tasks.