We present simultaneous measurements of acoustic emission and magnetic Barkhausen noise during the thermally induced martensitic transition in a Ni-Mn-Ga single crystal. The range where structural acoustic emission avalanches are detected extends for more than 50 K for both cooling and heating ramps, with a hysteresis of ∼10 K. The magnetic activity occurs during the structural transition, exhibiting similar hysteresis, but concentrated in the lower half of the temperature range. Statistical analysis of individual signals allows characterization of the broad distributions of acoustic emission and Barkhausen amplitudes. By studying the times of arrival of the avalanche events we detect the existence of correlations between the two kinds of signals, with a number of acoustic emission signals occurring shortly after a Barkhausen signal. The order of magnitude of the observed delays is compatible with the time needed for the propagation of ultrasound through the sample, showing correlation of some of the signals.