We address a multicriteria nonpreemptive energy-aware scheduling problem for computationalGrid systems. This work introduces a new formulation of the scheduling problem for multicore heterogeneous computational Grid systems in which the minimization of the energy consumption, along with the makespan metric, is considered. We adopt a two-level model, in which a meta-broker agent (level 1) receives all user tasks and schedules them on the available resources, belonging to different local providers (level 2). The computing capacity and energy consumption of resources are taken from real multi-core processors from the main current vendors. Twenty novel list scheduling methods for the problem are proposed, and a comparative analysis of all of them over a large set of problem instances is presented. Additionally, a scalability study is performed in order to analyze the contribution of the best new bi-objective list scheduling heuristics when the problem dimension grows. We conclude after the experimental analysis that accurate trade-off schedules are computed by using the new proposed methods.