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Side sleeping is fine if you know how to lie in the hammock properly (diagonally, unless it's a bridge hammock).
The travelpak sleeping bag @giofox88 mentioned is perfect for warmish weather hammocking since you can zip it around the hammock, too. (The footbox opens completely)
You can also just use a normal ground mat (inflatable, or otherwise) underneath you in a hammock. Works fine.
Are you not meant to be warmer as you're not on the ground?
But I've read very mixed reviews when it comes to hammocks so I may just get a tent and deal with it!