The Earth's climate has experienced dramatic changes over the past 22,000 years; however, the total meridional heat transport (MHT) of the climate system remains stable. A 22,000-year-long simulation using an ocean-atmosphere coupled model shows that the changes in atmosphere and ocean MHT are significant but tend to be out of phase in most regions, mitigating the total MHT change, which helps to maintain the stability of the Earth's overall climate. A simple conceptual model is used to understand the compensation mechanism. The simple model can reproduce qualitatively the evolution and compensation features of the MHT over the past 22,000 years. We find that the global energy conservation requires the compensation changes in the atmosphere and ocean heat transports. The degree of compensation is mainly determined by the local climate feedback between surface temperature and net radiation flux at the top of the atmosphere. This study suggests that an internal mechanism may exist in the climate system, which might have played a role in constraining the global climate change over the past 22,000 years.