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The gas is immediately mixed with the seal liquid (ring of water) and will leave the pump at the same temperature as the liquid:

An additional function of the seal liquid is to evacuate the heats, heat of compression and heat of condensation (most of the vapours are condensing during the compression). The compression is nearly isotherme.

The specific heat of the gas is nearly neglectible compared to the specific heat of the liquid of the ring. Liquid ring vacuum pump can handle hot gases, they are cooled down to the ring temperature.

Liquid ring vacuum pumps can handle vapours, not only because of their ability to handle liquids (condensate) but also because the seal liquid will evacuate the heat of condensation.