I've only been to NYC a couple times but I remember seeing a lot of homeless people. I'm sure that there are resources you could use to find out where the unsheltered homeless population in NYC sleeps, if it isn't in the parks.
Must be cooler there than on the ground.. Having lived through a few NYC summers, they can really be the worst. Not only it gets incredibly humid and hot, there's at least one serious rainstorm each week to drench you. I always found summer in NYC is much worse than winter.