Oh, and I would never actually use the copper cables with RJ45 for anything above 1 gigabit. Those ethernet cards heat up a lot, use too much energy. This would be a bad investment. Get a proper patch or optical cables and use SFP+ instead.
I’ve never had this as a problem, and I use 50-100ft of Cat5e + 10GBaseT SFP+’s… it’s well within the thermal limits of the SFP, which probably uses 2-5W.
I'm surprised you're able to get anything reasonable for 10G over any modest length of cat5e, i made a few attempts at doing it for fun when i was upgrading some of my stuff and could only get anything to work with cat6 at a minimum for more than a few meters.