Taking the Moving Average of STFT Results
As rb-j says in his comment, this is often how the (magnitude-squared) STFT is smoothed $-$ using a moving average window.

The only concern might be that you're using too much smoothing. A 10 second moving average window (resulting in a 12.5 second "effective" window) may mean that some artifacts take a while to show or do not show up at all.