If you want to know what the next couple of months will be like, you need only consult Hesiod's Works and Days:
In the season of wearisome heat, then goats are plumpest and wine sweetest; women are most wanton, but men are feeblest, because Sirius parches head and knees and the skin is dry through heat. But at that time let me have a shady rock and wine of Biblis, a clot of curds and milk of drained goats with the flesh of an heifer fed in the woods, that has never calved, and of firstling kids; then also let me drink bright wine, sitting in the shade, when my heart is satisfied with food, and so, turning my head to face the fresh Zephyr, from the everflowing spring which pours down unfouled, thrice pour an offering of water, but make a fourth libation of wine.
Which is, verbatim, what I'm going to say the next time I see a waiter.
That Sirus heats the earth is not true scientifically, but it is true poetically; and poetry is Much More Important than truth. If you don't believe that principle, try using the two methods to get laid.
Shakespeare mentions the Dog Days in Henry VIII. He describes a red-nosed fellow by saying:
There is a fellow somewhat near the door, he should be a brazier by his face, for, o' my conscience, twenty of the dog-days now reign in's nose;
Milton appears to mention the heat of Sirius in Lycidas:
Ye valley low where the mild whispers use
Of shades and wanton winds and gushing brooks,
On whose fresh lap the swart star sparely looks
Pope complains that "The Dog Star rages". But my favourite reference to the Dog Days is, for some reason, Fons Bandusiae by Horace. It's only a passing reference and it's in Latin but it translates very roughly as:
Sabine spring, as clear as glass,
Where the floating flowers pass,
Take tomorrow’s sacrifice
In your water cold as ice:
(For it grew its horns in vain,
For it will not breathe again)
Let the kid-goat’s hopeless blood
Mingle with your perfect flood.
No: the Dog Days’ horrid heat
Cannot touch you. Oxen’s feet
Stray from ploughshare to your pool,
Wander, rest there, and are cool.
Fame is yours, for I shall write –
And eternity recite
In perpetual murmuring tones –
Of the oak upon your stones.
However, as I said, the Dog Days have nothing to do with dogs and nothing whatsoever to do with Hamlet's comment that:
Let Hercules himself do what he may,
The cat will mew and dog will have his day.