An object will cool as long as it emits more energy than it receives. An object will warm as long as it receives more energy than it emits. Therefore, the heating or cooling of an object is cumulative. The amount of energy that has been taken away or received over a period of time determines how much an object will warm or cool. Take the earth's surface for example on a clear day. The sun has warmed the surface during the day. Once the sun goes down, the earth's surface will begin to cool (energy emitted is greater than energy received). This causes the earth's surface to become progressively cooler during the night. The earth's surface is not coldest right after sunset and not coldest in the middle of the night. It is coldest in the early morning hours around sunrise. This is because cooling is cumulative. The longer an object emits more energy than it receives, the more it will cool.
This idea of cumulative heating occurs on a clear day. The earth's surface is not the warmest when the sun is at the highest position in the sky (period of maximum daily insolation), the surface is warmest in the late afternoon, generally just 3 to 4 hours before the sun sets. The sun gradually warms the surface throughout the day. As long as the sun is supplying more energy than the earth can emit, the surface will warm.
The idea of cumulative heating also occurs on a global scale. Are ocean temperatures and average continental temperatures warmest in the beginning, the middle, or the end of summer? It is the beginning of summer when the sun is highest in the sky and the land and ocean surface has maximum insolation. Therefore, should the ocean and land temperatures be warmest at the beginning of summer? The answer is no. At the beginning of summer, the land and ocean surface are still recovering from the cooling they experienced over the winter. Should the ocean and land temperatures be warmest in the middle of summer? The answer is no for the ocean while yes for the land since the land is reaching peak warming. Even in the middle of summer, the accumulation of heat is still increasing the average ocean and land temperature. It is the late summer when ocean temperatures are warmest on average. This is why the hurricane season is not a peak in the beginning or middle of summer. It is August and September and even into October when most hurricanes occur. It is at this time the ocean temperatures are warmest. Land temperature warmth peaks before ocean temperature. It is middle summer when soil temperatures are warmest in the Northern Hemisphere. When Fall arrives, the sun's angle becomes low enough on the horizon that energy emitted from the surface begins to become greater than the incoming solar radiation (on a global scale). Longer nights and lower sun angles increase the amount of radiation that can be emitted from the surface. The accumulation of heat ends, and the ocean temperatures begin to cool and reach a maximum cooling in the middle to late winter. The land has maximum cooling typically in the first half of winter.