  We show that one can construct a quantum absorption refrigerator that
provides refrigeration only in the transient regime, by using three interacting
qubits, each of which is also interacting with local heat-bath. The machine
either does not provide cooling in the steady state, or the steady state is
achieved after a long time. We propose a canonical form of qubit-bath
interaction parameters that generates transient cooling without steady-state
cooling, and claim that such a phenomenon is generic to small-scale quantum
absorption refrigerators. We also show that it is generically possible to have
fast cooling. We demonstrate our results for two separate models of
thermalization, and show that a transient cooling without steady-state cooling
is associated with generation of negligible, or no bipartite quantum
correlations. For one of the models of thermalization, we find that the minimum
achievable temperature of the refrigerated qubit can remain almost frozen,
i.e., unchanged, for a significant region of the parameter space.
