  The process of thermalization in many-body systems is driven by complex
interactions among sub-systems and with the surrounding environment. Here we
lay the theoretical foundations for the active control of local thermal states
in arbitrary non-reciprocal systems close to their equilibrium state. In
particular we describe how to (i) force some part of the system to evolve
according to a prescribed law during the relaxation process (i.e. thermal
targeting probem), (ii) insulate some elements from the rest of the system or
(iii) synchronize their evolution during the relaxation process. We also derive
the general conditions a system must fulfill in order that some parts relax
toward a minimal temperature with a minimum energetic cost or relax toward a
prescribed temperature with a minimum time. Finally, we consider several
representative examples in the context of systems exchanging heat radiatively.
