(Facepalm) When I read this, I didn't register you'd said September. I was actually there in late September/early October (as well as briefly in August).
I don't remember being really cold, ever, which was different to Bolivia where it was FREEZING (below freezing) at the Salt Flats.
I assume if you did the Inca Trail you'd camp outside and get cold though - the temperature and oxygen drops dramatically as you go up. But the day I was on Machu Picchu it was hot, and I was in t-shirt and shorts (checks - it was October 4).
Lake Titicaca has a weird climate - in Puno, with a chance of a Thunderstorm in the late afternoons as the muggy weather changes. It was cool in the evening, but not cold.
I make fun of my friend from Lima by saying it's always 18C and semi-misty when I've been there. Turns out this isn't far from the truth, the Humboldt current causes it to almost always be cool as it brings the colder air in from the south, which surprises people who see it being close to the equator.
Mancora on the other hand - hot. On the beach, ALL day. Brilliant :)
Michael Smith's comment about Cuzco (and indeed Lima) is true - it's easy to buy warmer clothes - cheaply, just don't buy in the main squares. And baby alpaca wool is NOT actually from a baby alpaca - but it works well for selling to tourists ;) However the garments are all pretty good, and genuinely warm, I still use my jersey two years on.