Dog body temp is ~101-102.5 F (some go as low as 99.5 F). If your dog is 10 degrees hotter than you, you either have hypothermia or they have a severe fever.
We may be perceived as a little cooler than them but probably not "cold".
Oh dog, they meant Fathrenheits! I was thinking 10 degrees Celsius hotter, which sounded even more insane (that's 18°F if my math is correct).
Message to dear Americans: If you insists on using your freedom units, can you at least mark them properly? We have no way of knowing where you are from.
The way my dog squeezes his body and face into my leg to fall asleep (wiener dog), I'd say no. Keep in mind, we're still warmer than ambient temperature, so it's not like we're not pumping out heat.
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.