Abstract The Earth’s energy balance is crucial for maintaining a stable climate. Studies have shown accelerated net energy accumulation by the Earth in recent decades, mainly due to enhanced solar absorption. Meanwhile, observations show a pronounced increase in Arctic (north of 70N) outgoing longwave radiation (OLR), which acts as ‘radiator fins’ to radiate heat to space in a warming climate. However, how well global climate models (GCM) simulate such effect and what drives model biases remain unclear. Here, we compare Arctic OLR trends from GCM simulations and reanalysis and find most models underestimate Arctic OLR trend, which arises from too weak a surface warming trend and too strong a dampening effect of atmospheric moistening. Notably, models with stronger Arctic OLR trends tend to simulate greater Arctic amplification, whereas models with weaker trends generally have lower future global surface warming, suggesting that present‐day Arctic OLR trends may constrain future climate projections.