I put together a list with suggestions and links several months ago, here are some hot weather-specific items:

The #1 most essential item I can possibly recommend: WATER WIPES! These are essentially like baby wipes or facial cleansing wipes or makeup remover wipes, except instead of a regular cleansing solution they contain only 99% water, with the remaining 1% being something called soapberry extract, which is a berry that has natural surfactant properties and foams up like soap when you scrub with it. I remembered packing tons of these things when I used to work at Amazon, so when we found ourselves living out of a tent, I experimented with several different kinds and determined these to be the superior brand. These fragrance-free ones in the blue package are unscented and completely residue-free. (There are a lot of review on the Target website complaining that the formula has recently been changed, but at least in my area I don't notice a difference - so don't pay attention to the star rating!) Most cleansing wipes leave a sticky film on your skin, but these are as close as you can possibly get to washing with plain H2O. A single 20-sheet pack is just $0.89 cents in the travel-size section. Believe me when I say these things will improve a homeless person's quality of life exponentially.

The link: Up & Up Fragrance-Free Baby Wipes

Okay moving on...

Microfiber cooling towels: soak in water, wring out and they'll keep you cool for hours. This pack contains 20 at about $1.00 a piece.

First aid items, including Band-Aids, gauze and topical antibiotic ointment. These small packets of triple antibiotic gel are about nine cents per packet, a box of 144 is $13.45.

Mylar space blankets for cold nights and emergencies - these are about $1.25 per blanket - and fleece blankets for sleeping and everyday use - these are about $4.85 per blanket. Even in summer weather and in climates where the temperatures are warm year-round, for example desert climates like in the American southwest, it can still get dangerously cold at night. These space blankets are literally a lifesaver.

Electrolyte powder drink sticks, mix directly into bottled water or any other beverage, will help prevent dehydration which is a serious risk for individuals who are homeless during extremely hot weather, especially if it can be difficult to find shade or shelter from the sun. These are very cheap, $2.79 for a box of 10 or $0.28/ea, so throw in a whole handful.

Aluminum-free antiperspirant. It costs a few cents more for the kind without aluminum, but do try to swing it if at all possible as so many people are allergic to it, causing terrible skin reactions that can be exacerbated by hot weather. These travel-size Dove sticks are about $1.15/ea or $48 for a pack of 36.

Travel-size hand sanitizer, about $0.55/ea or $32 for a box of 72.

SPF 30 sunscreen, a box of 100 individual packets for $23.

Mini SPF 15 lip balm, assorted flavors (it's important to remember to use sunscreen on the lips as they can easily get burned!) - these are about $0.58/ea.

Aloe vera sunburn gel, $0.89/ea or $8.99 for a box of 10 individual packets.

Dry shampoo, if you can afford it. These full-size cannisters are about $4.50/ea on Amazon, but you can usually find the travel-size ones for much cheaper in your local dollar store. Again, not a necessity, but it can make a huge difference for women and men with long hair who may have to go long stretches of time between washing their hair.

I also suggest using polyester bags instead of canvas ones as they hold up better against moisture and tend to be more durable. We were always grateful when we received one of these things and were usually able to reuse it for quite awhile. These drawstring backpacks are about $1.00 a piece.