Depending on energy sources and demand, the carbon intensity of the public power grid fluctuates over time. Exploiting this variability is an important factor in reducing the emissions caused by data centers. However, regional differences in the availability of low-carbon energy sources make it hard to provide general best practices for when to consume electricity. Moreover, existing research in this domain focuses mostly on carbon-aware workload migration across geo-distributed data centers, or addresses demand response purely from the perspective of power grid stability and costs. In this paper, we examine the potential impact of shifting computational workloads towards times where the energy supply is expected to be less carbon-intensive. To this end, we identify characteristics of delay-tolerant workloads and analyze the potential for temporal workload shifting in Germany, Great Britain, France, and California over the year 2020. Furthermore, we experimentally evaluate two workload shifting scenarios in a simulation to investigate the influence of time constraints, scheduling strategies, and the accuracy of carbon intensity forecasts. To accelerate research in the domain of carbon-aware computing and to support the evaluation of novel scheduling algorithms, our simulation framework and datasets are publicly available.