So.. From what I can tell it looks like I need a new thermostat. Radiators start to heat up as soon as I turn the bike on, and getting it anywhere near operating temperature is impossible outside of city traffic. And big surprise, new thermostats for a nearly 20 year old bike are not easy to find. Or rather, they are not easy to find with that model name/year on them. But I'm pretty sure it's like many other things and they used the same one for many bikes over many years. So the question is; Which bike models and years use the same thermostat? Knowing the compatibility would make finding one much easier.
Still available at any Honda motorcycle spare parts. I don't know of any non Honda bike one that will fit.
Thank you. I guess I'm so used to working on older bikes or bikes where parts are hard to come by, that it never even occurred to me that the original part might still be in production. In any case. I ended up taking it to the shop. When I looked closer at the work involved, I decided it wasn't worth the trouble trying to do it myself. Took the mechanic a while, but it's done and works perfectly. In the few tanks of fuel I have had through it since, it looks like it is slightly less thirsty after the operation. Is that a common "side effect".
If the bike is not getting to running temperature, the fuel injection will keep running rich so economy will suffer.