I've spent a few weeks in Tokyo and Kyoto mid summer (though less extreme I guess than this summer) and you can "manage"--in the sense that you can limit activities during the hottest parts of the day or just in general--but I don't really recommend picking visits at those times unless you have some specific reason to.

Montreal in winter on the other hand is fine. But, as you say, you need the right clothing which can be reasonably compact but isn't going to fit in tiny luggage. (And activities will be at least somewhat different from in summer.)

I'm a fairly compact traveler in general (just carry-on usually) and you can get off with a lot in temperate to warm climates in urban locations where you don't need to dress up. But I also don't like to pack only those things that I'm sure I need. For example, I have a little kit bag of miscellaneous stuff I mostly don't need but am sometimes glad I have.