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We investigate a stochastic heat engine based on an over-damped particlediffusing on the positive real axis in an externally driven time-periodiclog-harmonic potential. The periodic driving is composed of two isothermal andtwo adiabatic branches. Within our specific setting we verify the recentuniversal results regarding efficiency at maximum power and discuss propertiesof the optimal protocol. Namely, we show that for certain fixed parameters theoptimal protocol maximizes not only the output power but also the efficiency.Moreover, we calculate the variance of the output work and discuss thepossibility to minimize fluctuations of the output power.

Exactly solvable model of stochastic heat engine: Optimization of power, its fluctuations and efficiency