When watering my sunchokes I notice they get as cold as the water going on the plants. Why is the water cooling the plant so quickly instead of over time, and not staying at about the same temperature of the air, or the surface of the soil?
It is physics, not botany.
Water usually is colder then ambient (not really, it is just above the mean yearly temperature, which happens to be much cooler that one think, and it is lower than the day temperature). In general ground and water keep temperature more constant, so more you dig, less temperature changes you have. Around 10m (30ft) you have temperatures that don't change nor during day, nor during the year, so it is very like the mean temperature). Water pipe are installed on ground, so they are cooler than day.
There is also an additional reason. Vapor have much more energy than water, so, in order to evaporate, water take heat from ambient. One could try in the shower, with water temperature constant, changing the water stream size, it will change the "apparent" temperature. Firefighters use vaporizers also for this reasons.
So, if you need to water a plant, water the ground, with relatively large drops, or just a regular flow. If instead you need to control the temperature (it is done e.g. on tomatoes in greenhouses), very small drops will reduce temperature, and they will also evaporate quickly, so without increasing risk of deseases.