I d’know “the countryside is the absence of a city” kindof -is- what heat is, in an abstract way. Water is probably a better metaphor, a cold object is like an empty lake, if you connect it to a full lake, the water will flow in rapidly at first, then slow down as the level of water gets more similar between the two bodies. In a related way, the less water you have in your lake, the harder it is to remove, since you need a more empty lake to extract that water, and the removal will be slower since the level is similar between empty and almost empty.
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