  We show theoretically how the periodic coupling between an engineered
reservoir and a quantum Brownian particle leads to the formation of a dynamical
steady state which is characterized by an effective temperature above the
temperature of the environment. The average steady state energy of the system
has a higher value than expected from the environmental properties. The system
experiences repeatedly a non-Markovian behavior -- as a consequence the
corresponding effective decay for long evolution times is always on average
stronger than the Markovian one. We also highlight the consequences of the
scheme to the Zeno--anti-Zeno crossover which depends, in addition to the
periodicity $\tau$, also on the total evolution time of the system.
