No. When the coolant is shoved through the micro-fins inside the pump housing, it picks up heat energy which is transfered to hose and the radiator fins. Where it gets dissipated, transfered to the surrounding airflow. It takes a massive, constant amount of energy to heat up liquids, even as little as 1°C. The coolant can take upto half an hour to warm up 1°C, depending on the wattage output of the cpu.
If in doubt, slap some water in a pot on low heat and see how long it takes to get a little warmer, that's about the same output wattage as a cpu. A burner on high is putting out 1500w+.
Its the latent heat energy the liquid is moving, not any actual heat. The hose gets warmer because it has little in the way of being able to dissipate the heat energy, so that energy sticks around and warms up the hose. But the actual coolant is almost the same temp coming out as it is going in, which is why in custom loops it doesn't matter where the radiator is in regards to loop position.