You can run a 12v coolbox on an adaptor on ehu for days on end, it works well enough although I would only use it for drinks cooling not meat or cheese. A cheap coolbox will cool to about 18degC below ambient whatever that is & you cannot adjust it which means in southern France 30+ temps it might not be that good & on cold UK nights it can freeze it's contents, so you might have turn it off overnight.
If weather is fairly warm, for best results put your drinks in at night to cool down but don't replace as you drink them until next evening. If you replace with warm cans during day it will raise temps of the cold drinks already in there.
Have to agree the Campingaz/Coleman adaptor is the best one to go for had ours on various coolboxes and never had any problems with it, the 12v lead plugs straight into it
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