Power cool-boxes or thermo electric coolers use 12v or mains power to maintain a temperature below the ambient Air temperature. They do not work in the same way as a fridge.
Dependant on the model that maintain a temperature generally 16 to 20 degrees below the ambient air temperate. Therefore the temperature will fluctuate within the cool-box. So if you position our cool-box in a hot vehicle or tent the cooling performance will be less than if the cool-box is positioned and used in a shaded or cooler area.
Thermoelectric coolers work well of 12v power but are quite heavy users of power so be careful if using your vehicle battery. Some models have built in circuits that switches off the power when it detects the 12v supply voltage dropping.
Again some models have built in 230v connections or you can purchase optional 12v/230v transformers to use your cool-box on the 230v supply on site or at home. These can be found under the accessories section.