A correlated imaging system with flexible frame rate was proposed and fabricated on the Field Programmable Gate Array (FPGA) for acquiring temperature images. Real-time images of temperatures are reconstructed on chip at a frame rate of 10 Hz, and higher rates up to 1280 frames per second are also achieved in case of resolution sacrifice. Compressive sensing method enables the flexible frame rate for dynamic temperature images. An incandescent filament was imaged and compared by the proposed imaging system and a commercial Charge-Coupled Device (CCD) camera. Reconstructed images of temperature distributions agreed well with those from the camera in the range from 1500 K to 2500 K. Moreover, the proposed system captured the excitation frequency of an acoustically excited flame by varying the frame rate. The simple structure and flexible frame rate provide an alternative to dynamical temperature imaging, especially in case the common CCD camera fails to work for its slow response.