It is clear that the exhaust gas should be relatively cool after the water injection elbos and much cooler after the waterlift muffler (assuming you have one). Basically the heat capacity of water is about 2.5 time larger than that of exhaust gasses on a per mol basis. For a normal small diesel system, the number of mols of water is large compared to the number of mols of exhaust gas, so the water will cool the gas very effectively. Furthermore, the exhaust gases cool a lot simple due to expansion after they leave the engine cylinder. Of course the ultimate cooling effect comes fom vaporizing some of the cooling water where the heat required to vaporize water is 535 times larger than the heat capacity of liquid water