It's awful isn't it??? My baby was born on 11th July last year and it was so hot, I was convinced she wasn't going to survive! I remember looking at other people's older children walking around in their sun hats and summer clothes and wondering (tearfully) how they'd managed to stay alive, and more to the point, how I was going to keep my newborn going ... looking back on it, I can see how crazy my post-partum thoughts were to begin with!
Anyway, she's still here. In those first couple of sweltering months, she spent a lot of her time feeding in a nappy in front of an air-con unit, or a fan. She slept in just a nappy, with the air-con going. If a blanket was needed, we used a muslin cloth to keep air circulating. A Gro Egg thermometer helped us keep an eye on just how warm it was getting in our room.
I'd say offer offer offer - breast or bottle, whichever you are using, because dehydration is a bigger worry than anything in this heat - keep an eye on his nappy output. Keep clothes to a minimum, or don't dress him at all. Maybe get one of those little handheld fans for when you're out and about. Keeping him in the shade, like you are, is best, and the less time spent in sweaty car seats/strollers the better! A tepid bath, maybe 1-2 degrees below the recommended 37 might be nice for him, as long as he isn't in there too long.
Finally, at the end of the day, the heat will pass. Making sure he is hydrated and as cool as possible, especially at night, is the most important thing.