Beating heart cells, cardiomyocytes, are used in drug testing and have the potential for regenerative medicine. Currently their classification into atrial, nodal and ventricular subtypes is performed using destructive and tedious patch clamp measurements. We present a method for analyzing cardiomyocyte contraction cycles using diffraction phase microscopy, a fast quantitative phase imaging method based on off-axis common-path interferometry. The phase variation during the beating cycle can exceed 300 mrad in the most active regions, and is about 40 mrad on average. The phase noise is about 2 mrad per pixel, and it can be reduced by temporal averaging over multiple frames and spatial averaging over the cell. With a maximum acquisition rate exceeding 25,000 fps and with approximately 100 fps required for the characterization of cardiomyocyte motion, 250 frames can be averaged per step, reducing the temporally white noise by a factor of 16. Additional improvements can be obtained by averaging over multiple contraction cycles. Averaging over space does not reduce noise to the same extent due to low-pass spatial filtering during the phase extraction procedure. Low-pass filtering by the pinhole in the reference arm, resulting in high-pass filtering of the image, and low-pass filtering during the phase reconstruction highlight the dynamics of redistribution of dry mass within the cell during a beat cycle. Quantitative phase imaging is a promising approach for rapid, non-invasive, high-throughput characterization of human stem cell-derived cardiomyocytes in culture, with applications to modeling of diseases with patients' specific genes, drug development, and repair of damaged heart tissue.