While it is true that higher intake temperatures for internal combustion engines will ingest air of lower density, this only holds correct for a static, unchanging air pressure. i.e. on a hot day an engine will intake less oxygen per engine cycle than it would on a cold day. However, the heating of the air, while in the supercharger compressor, does not reduce the density of the air due to its rise in temperature. The rise in temperature is due to its rise in pressure.