Accurately predicting the power consumption and latency of software applications deployed on multicore platforms is a critical bottleneck for early-stage performance optimization, as it often relies on slow and costly simulations. To address this challenge, we introduce a graph-based methodology that models the mappings of software applications onto multicore architectures as heterogeneous graphs. We then investigate Graph Neural Networks (GNNs) to predict power consumption and latency for these mappings. Four classes of state-of-the-art GNNs were trained under various conditions on 11 datasets, each containing multiple mappings of a given Neural-Network application. The two best-performing GNN classes achieve mean absolute percentage errors of around 2% for power-consumption prediction and 15% for latency. Inference requires only a few tens of milliseconds per prediction. This work demonstrates that GNNs offer a fast and promising approach to performance prediction, opening the door to AI-assisted optimization of software mapping on multicore platforms. The relevance of our work extends beyond the use case: we introduce an operational framework for GNNs to support heterogeneous graph processing and multi-output regression at the graph level.