According to Wikipedia:
"Originally, the phrase, 'Dog Days' had nothing to do with dogs, or even with the lazy days of summer. Instead, it turns out, the dog days refer to the dog star, Sirius, and its position in the heavens.
To the Greeks and Romans, the 'dog days' occurred around the day when Sirius appeared to rise just before the sun, in late July. They referred to these days as the hottest time of the year, a period that could bring fever, or even catastrophe."
Culturally, the phrase has taken on its own meaning of "the hot sultry" days of summer. Here in Phoenix, when it gets hot in July & August (generally our hottest days) there are warnings everyday about not leaving your dog (or baby) inside a car on a hot day, the temperature inside the car can, in many cases cause death.
At 70 degrees on a sunny day, after a half hour, the temperature inside a car is 104 degrees. After an hour, it can reach 113 degrees. When temperatures outside range from 80 degrees to 100 degrees, the temperature inside a car parked in direct sunlight can quickly climb to between 130 to 172.
Another dog phrase often used is, "I wouldn't put a dog out on a night like that!" Meaning that conditions are so bad that putting the dog out would be disaster. From which came the "shaggy dog" story (shortened here) regarding King Arthur who saw Sir Lancelot on a horse that had been ridden to exhaustion and said, "I wouldn't put a knight out on a dog like that!"
So, during these last few dog days of summer, keep cool, look to the stars for inspiration, enjoy the puns and don't be so Sirius!