  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 cavity's 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} $.
