This is not really accurate. To get meaningful emissions from normal electrodes, you need to heat them up to about 2000 °C. Vacuum tubes operate at 700 °C or something like that. The trick is that one electrode is doped with special rare-earth additives that greatly increase electron emissions. The same treatment isn't applied to the rest of the device. So, even if all internal components have the same temperature, a vacuum tube can still work (to some extent).