Do linen sheets actually keep you cool in summer?

Yes, with caveats. Linen's loose weave and moisture-wicking flax fiber are why hot sleepers in r/Bedding and r/BedroomBuild threads repeatedly recommend it. That said, some Reddit users note linen can feel warmer than percale cotton in dry climates because it holds body heat against the skin when there's no humidity to wick. For humid summer sleepers, linen is hard to beat; for very dry climates, a crisp percale may sleep cooler.