Like most other people, I once thought that Dog Days did indeed have something to do with dogs. I eventually learned that no, they acquired their name from Sirius, the Dog Star, which is at its brightest during certain weeks in summer. The Ancient Greeks (some sites credit the Romans, so you can take your pick) believed that during these weeks when the sun and Sirius rise and set together, the two combine to make us all hotter than ever.
Nowadays, due to the Earth’s “wobble”, the Dog Days fall later than in the time of the Ancient Greeks. This progression will continue, so that at some time far into the future, the Dog Days will fall in the middle of winter!