I’m very much a newbie here, but I’ve got a lot of (bad) experience with sleeping hot and “cooling” bedding.
Your 2nd option, the “cooling” sheets made of polyester? Won’t be cooling. They may feel slightly cool to the touch when you first slip into bed. But they will heat to the temperature of a small sun once you’ve been laying on them for a bit. Polyester doesn’t breathe. At all. There’s nowhere for your body heat to go in those sheets, except right back at you. If you sleep warm, polyester is not your friend. They will probably feel soft, however.
As for the bamboo-rayon sheets. They’ll feel soft and very smooth. Almost slippery, in fact. I had a hard time keeping my pillow inside the pillowcase, it kept trying to slide right out. Not sure for how long it’ll feel that smooth before the fabric starts to pill, however - I didn’t like mine enough to keep them long-term. They might feel a bit cooling. (The ones I tried were bamboo viscose, which is similar, but not quite identical. They were moderately cool in that they didn’t trap too much heat, but I found them clingy and sort of “sticky” once I got a bit sweaty.) They have oodles of positive reviews, so they’re clearly working for some people! I’m just not one of them.
Basically, my experience tells me that anyone who’s promising cooling with synthetic fibers isn’t telling you the full truth. To sleep more cool, I’ve found that natural materials work best, because they breathe. For sheets, I’d look at cotton (specifically a percale weave) and linen. Both will be light and breathable around you. There’s only so much they can do if your room is super warm, or if you’re bundled under a heavy blanket, or if you’re sunken 2" deep into a memory foam mattress. But if you’re running the a/c and/or have a fan going for comfort and you’re reasonably covered otherwise, those materials will absorb your sweat and pull it away from your body along the fibers in the fabric. And they will let your excess heat dissipate through the spaces in the weave. Neither will be silky, though a good percale should be light, airy, and crisply smooth. Cotton sateen isn’t a bad idea either, but too warm for me to personally recommend. If you only sleep a little hot, sateen weave cotton will be almost as smooth as those bamboo rayon sheets, and likely hold up better, as well. For either percale or sateen, reasonable quality at a reasonable price, I’d suggest taking a look at California Design Den. They sell via Amazon as well.
If you’d like a good splurge, go for linen, or even silk sheets. Linen will always be textured, definitely not smooth, but is nonetheless soft, and gets softer and softer with wear and washing. Silk is literally silky smooth. Both are breathable and a nice upgrade, if you can swing the costs.
I hope you find what helps you sleep well.