Climate forcings by greenhouse gases and aerosols cause an imbalance at the top of the atmosphere between the net incoming solar radiation and outgoing longwave radiation from Earth. This Earth energy imbalance has strengthened over the period 2001 to 2023 with satellite data. Here, we show that low climate sensitivity models fail to reproduce the trend in Earth energy imbalance, particularly in the individual longwave and shortwave contributions to the imbalance trend. The inability to produce a strong positive shortwave and strong negative longwave Earth energy imbalance trend is found to be a robust feature in the low climate sensitivity models, especially for models with a climate sensitivity below 2.5 kelvin. The negative longwave contribution to Earth energy imbalance is driven by surface temperature increases and is therefore most pronounced in high climate sensitivity models, whereas the shortwave contribution is generally positive and amplified by greater surface warming.