Is the ionosphere the place where the troposphere stops getting colder?

No, the ionosphere is not where the troposphere stops getting colder. The troposphere is the lowest layer of Earth's atmosphere, where temperatures generally decrease with altitude until reaching the tropopause, the boundary between the troposphere and the stratosphere, which is typically where temperatures start to stabilize or increase. The ionosphere, on the other hand, is a region of the upper atmosphere, above the mesosphere, that contains ionized particles and is influenced by solar radiation.