It depends on whose temperature you are to describe, maybe therefor you wrote that " many words".
"Ondo" is just a general idea.
If you catch cold and then have to describe your body temperature, we will never say "karada no ondo" but "tai-on" 体温
For the cilimate, usually "ki-on" will be used. 気温
For swimming in the pool, river or in the ocean, "sui-on" will be used to mention, if the temperature is warm enough for swimming. 水温
For every case, only "on" will be added to the substance of interest. Do not add "do" to it.