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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.
Not only is the insulation squished (and moved around) but I think the bigger factor is the wind chill (even if there is virtually no breeze) that efficiently moves fresh air past your bottom the whole time.
Side sleepers need not apply either.