It's quit simple actually. The "hot" part came from it being served hot. The "dog" part came from it's resemblance to a Dachshund those long skinny dogs like the one in Toy Story. Which put together...
The term "hot" is used because the meat is cooked.The term "dog" has been used as a synonym for sausage since at least 1884 and accusations that sausage makers used dog meat date to at least 1845.I...