Near-field heat radiation and transfer are rich in various exciting effects, in particular, regarding the amplification due to the geometrical configuration of the system. In this paper, we study heat exchange in situations where the objects are confined by additional objects so that the dimensionality of heat flow is reduced. In particular, we compute the heat transfer for spherical point particles placed between two parallel plates. The presence of the plates can enhance or reduce the transfer compared to the free case and provides a slower power-law decay for large distance. We also compute the heat radiation of a sphere placed inside a spherical cavity, finding that it can be larger or smaller compared to the radiation of a free sphere. This radiation shows strong resonances as a function of the cavitys size. For example, the cooling rate of a nanosphere placed in a cavity varies by a factor of $10^5$ between cavity radii $ 2 mu {rm m} $ and $ 5 mu {rm m} $.
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