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Heat transfer works both ways - so if they feel you as cold then you’d feel them as warm. In my experience dogs usually don’t stand out to me as being particularly warm so I’d guess their fur is a good enough insulator to prevent much heat transfer during normal casual contact. It’s been a few months though, maybe I’ve just forgotten how warm the embrace of a dog is.
$1000 to someone with $100,000 is like $1,000,000 to someone with $100,000,000. To make your point you’d have to do it backwards: $1000 to someone with $100,000,000 is like $1 to someone with $100,000.