Phase change is actually not the same as a TEC, or Peltier.
Thermoelectric coolers CAN do a great job but they actually increase the heat load of the SYSTEM. The chip being cooled will be cooler, but the exhaust air will be considerably warmer. A LOT warmer.
Phase Change is the process of compressing a gas to a liquid state and then suddenly releasing it to expand- the sudden expansion (the Phase Change) provides cooling. This is how air conditioners and refrigerators work.

In computing, Phase Change is most commonly put into use as Direct Die Phase Change:
the chamber where the expansion (and cooling) occurs is mounted on the cpu, just like a heat sink. ALL of the refrigerant power is put to use to cool JUST the cpu.
This is VERY effective and can easily result in subzero temperatures under full load.
But in a car computer.... yeah, not so effective. A compressor will either rob engine power (belt driven like car ac) or electric load on the battery- and it will generate a LOT of heat.
Air cooling is definitely the simplest and can USUALLY be done successfully with planning and care, and maybe a few low noise fans.
Water cooling is a bit more complex, but if you are struggling with air cooling, and trying to figure out how to duct intake and exhaust air to keep the system stable, it may not be much more complex.
*Modern pumps add little heat to the system and run on 12v (computer psu.)
*1/2" Inside Diameter tubing is most common in High Performance water cooling, but 3/8" or even 1/4" ID can do a decent job in a system that is not highly overclocked.
And small tubing is easy to route.
A few points though:
Water cooling still depends on Ambient Air to cool the radiator down- it just makes it easy to relocate WHERE you send that warmth.
Water cooling will NOT cool everything in a system like Air Cooling does: only the chips with water blocks will be cooled. (Other components will benefit from the LACK of all that extra heat nearby.)
Some airflow is still required to cool motherboard components such as chipsets, voltage regulators and memory.