We present an experimental study of the transformation avalanches taking place during a thermally induced thermoelastic martensitic phase transition of a Cu-Zn-Al alloy. We have studied the statistical distribution of amplitudes and durations of the acoustic emission signals released in the avalanches and found them to exhibit power-law behavior in more than one decade. Distributions measured around different temperatures along the transformation path are found to be equivalent. We have measured the exponents for the distribution of amplitudes (α=3.6±0.8) and durations (τ=3.5±0.8), for the statistical dependence of amplitudes on durations (x=1.0±0.1) and for the power spectrum of trains of measured acoustic signals (φ=0.9±0.1).