I think it’s about insulation which involves trapping air in this case. The T-shirt material has looser fibers because it is knit. Microscopically it is probably coarser which provides lots of little pockets for air to settle. That air traps heat. Your Egyptian cotton sheets are probably woven and have a very tight, fine structure. This makes for a smoother surface and less trapped air.
In general smooth fabrics are cooler than soft fluffy fabrics. Synthetics are especially cool to the touch because they are plastic. But sometimes you want natural fibers for their wicking and breathing properties.
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