I may have missed your point slightly in relation to non-coding versus protein coding genes. If you have conducted your entire analysis separately for protein coding genes and non-coding genes (that is, normalisation and differential expression analysis separately), then it is my view that they also should be shown separately in different heatmaps.
There is no problem conducting your analysis by just focusing on protein coding genes alone, and there is neither a problem focusing on protein coding + non-coding combined.
As you can see, there are no rules here... you can present your results in the way that helps to get the information best to the reader.