  Superconducting quantum circuits are potential candidates to realize a
large-scale quantum computer. The envisioned large density of integrated
components, however, requires a proper thermal management and control of
dissipation. To this end, it is advantageous to utilize tunable dissipation
channels and to exploit the optimized heat flow at exceptional points (EPs).
Here, we experimentally realize an EP in a superconducting microwave circuit
consisting of two resonators. The EP is a singularity point of the Hamiltonian,
and corresponds to the most efficient heat transfer between the resonators
without oscillation of energy. We observe a crossover from underdamped to
overdamped coupling via the EP by utilizing photon-assisted tunneling as an
\emph{in situ} tunable dissipative element in one of the resonators. The
methods studied here can be applied to different circuits to obtain fast
dissipation, for example, for initializing qubits to their ground states. In
addition, these results pave the way towards thorough investigation of
parity--time ($\mathcal{PT}$) symmetric systems and the spontaneous symmetry
breaking in superconducting microwave circuits operating at the level of single
energy quanta.
