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Quantum heat engines are modeled by thermodynamic cycles with quantum-mechanical working media. Since high engine efficiencies require adiabaticity, a major challenge is to yield a nonvanishing power output at finite cycle times. Shortcuts to adiabaticity using counter-diabatic (CD) driving may serve as a means to speed up such, otherwise infinitely long, cycles. We introduce local approximate CD protocols for many-body spin quantum heat engines and show that this method improves the efficiency and power for finite cycle times considerably. The protocol does not require a priori knowledge of the system eigenstates and is thus realistic in experiments.