I’m retired now but at my last work place they ran cat 5 through the building ducts and it was a huge improvement over the previously horrible WiFi that we had. There were no issues over the year and a half of use before my retirement. I chatted with installer who said that they do this all the time. He said that he had never encountered an issue with warping due to HVAC, which was the first question that I asked.
Ethernet cable is inexpensive. Even if something did warp after years of use, replacing it should not be to painful