When you say the pic tube is still cold, does that mean the heater is not lit?
The CRT neck does not run hot at all compared to the power tubes, damper and 5U4 which opererate under heavy current and run very hot.
If you're not getting a raster, have you adjusted the ion trap to find the elusive 'sweet spot' that makes the raster appear? If not, Rotate the trap around a full 360 degrees, slide it forward and back, and if nothing appears, swap it end for end and repeat.
Even if the CRT has weak emission you should stiil get a visible raster since the little tube made a raster.