A new approach for broad and efficient tuning of the narrow resonant transmission window in integrated phase shifted Bragg gratings realized in silicon waveguides, suitable for the photonic processing of microwave signals, is proposed and demonstrated. The method exploits local micro-heaters (MHs) for the tuning of the resonant cavity formed by the insertion of a phase-shift section within a uniform Bragg grating structure. Two different MHs geometries have been investigated. Wide tuning ranges of the passband filter with a narrow linewidth of 30 pm up to 7 nm, only limited by the BG stopband region width, for maximum MH absorbed power of 11 mW are observed.