Trip to Greece and Turkey - September or august??

August will be very hot. Considering that you are from Canada (where it doesn't get blisteringly hot and humid), I wouldn't do it, personally. On the other hand, if it is a matter of not going at all, or dealing with the heat, I would still go. Regarding what to see and do, your interests should be defined so that we can give you some ideas. Turkey and Greece are both fascinating places to visit.

"Considering that you are from Canada (where it doesn't get blisteringly hot and humid)" Hah!

The month of August is the holy month of Ramadan this year. We happened to visit Istanbul during Ramadan a few years ago and we enjoyed it very much. After sunset, the Sultanahmet area became a street festival, with scores of temporary booths selling all kinds of food, the streets full of people of all ages, colored lights everywhere, a real carnival atmosphere. It was a lot of fun and as non-Muslims we were totally welcomed to share in the celebration. So based on our experience, if Istanbul is on your itinerary, I'd encourage you to visit there in August.

In addition to the heat, Greece in August is very, very crowded with tourists. I'm not sure if it's as bad in Turkey, but I suspect it is. If August is your only possible time to go, start your trip as late in August as possible, and make sure your hotels are air conditioned. Skip the Cyclades (Santorini, Mykonos) and focus on the smaller, less touristed islands along the Turkish Coast (the Dodecanese and Northeastern Aegeans). These islands are closer to Turkey as well, so it makes an easier trip to plan. Three weeks is not enough time to see both countries. If that's all you have, you should probably focus on the one you're most interested in (i.e. either Greece or Turkey), with a day trip or two to the other. There are about a half-dozen Greek/Turkey ferry connections available. For a three week trip to Greece, it might be best to fly into Athens and then directly to an island. Then fly back to Athens a couple of days before your flight home, saving your Athens sightseeing for the end of your trip. If you have four weeks, you could fly into Athens, and spend 2 nights there seeing the sights. Then fly or ferry to an island for 2 or 3 nights. Visit another small nearby island for a couple of days, and then go by ferry into Turkey. Visit a couple of places in Turkey, and end up in Istanbul, flying home from there.

Either month should be fine for Turkey. August will be hotter. I don't think crowds will be too different between the two months. Tom has a good observation about Ramadan. It would be a unique experience - especially if you're there at the very end of the August for the Bayram/Eid. I'll let those with more experience in Greece comment for that country. Good luck.