Marine heatwaves (MHWs), an extreme climate phenomenon, pose significant challenges to marine ecosystems and industries, with their frequency and intensity increasing due to climate change. This study introduces an integrated deep learning approach to forecast short-to-long-term MHWs on a global scale. The approach combines graph representation for modeling spatial properties in climate data, imbalanced regression to handle skewed data distributions, and temporal diffusion to enhance forecast accuracy across various lead times. To the best of our knowledge, this is the first study that synthesizes three spatiotemporal anomaly methodologies to predict MHWs. Additionally, we introduce a method for constructing graphs that avoids isolated nodes and provide a new publicly available sea surface temperature anomaly graph dataset. We examine the trade-offs in the selection of loss functions and evaluation metrics for MHWs. We analyze spatial patterns in global MHW predictability by focusing on historical hotspots, and our approach demonstrates better performance compared to traditional numerical models in regions such as the middle south Pacific, equatorial Atlantic near Africa, south Atlantic, and high-latitude Indian Ocean. We highlight the potential of temporal diffusion to replace the conventional sliding window approach for long-term forecasts, achieving improved prediction up to six months in advance. These insights not only establish benchmarks for machine learning applications in MHW forecasting but also enhance understanding of general climate forecasting methodologies.