"The entire tube, inside and out, will eventually reach the same temp whether heated from within or from outside."
From that unimpeachable source, Wikipedia:
"Vacuum tubes require a large temperature difference between the hot cathode and the cold anode. Because of this, vacuum tubes are inherently power-inefficient; enclosing the tube within a heat-retaining envelope of insulation would allow the entire tube to reach the same temperature, resulting in electron emission from the anode that would counter the normal one-way current. Because the tube requires a vacuum to operate, convection cooling of the anode is not generally possible unless the anode forms a part of the vacuum envelope (in which case the cooling is by conduction through the anode material and then convection outside the vacuum envelope). Thus anode cooling occurs in most tubes through black-body radiation and conduction of heat to the outer glass envelope via the anode mounting frame. Cold cathode tubes do not rely on thermionic emission at the cathode and usually have some form of gas discharge as the operating principle; such tubes are used for lighting (neon lights and neon glow lamps) or as voltage regulators."
From that unimpeachable source, Wikipedia:
"Vacuum tubes require a large temperature difference between the hot cathode and the cold anode. Because of this, vacuum tubes are inherently power-inefficient; enclosing the tube within a heat-retaining envelope of insulation would allow the entire tube to reach the same temperature, resulting in electron emission from the anode that would counter the normal one-way current. Because the tube requires a vacuum to operate, convection cooling of the anode is not generally possible unless the anode forms a part of the vacuum envelope (in which case the cooling is by conduction through the anode material and then convection outside the vacuum envelope). Thus anode cooling occurs in most tubes through black-body radiation and conduction of heat to the outer glass envelope via the anode mounting frame. Cold cathode tubes do not rely on thermionic emission at the cathode and usually have some form of gas discharge as the operating principle; such tubes are used for lighting (neon lights and neon glow lamps) or as voltage regulators."