> In a vacuum, not much heat is transfered?
I suspect this is a non-issue.
Obviously the normal condition is both heaters cooking, which raises both cathodes' temperature. So one heater alone must run cooler.
Our first rebuttal is that oxide heaters just are not fussy. They make 100 times more electrons than we need. The grid passes one electron and returns the excess 99 electronsto the cathode cloud. If some less-heat condition makes only 90 times more electrons than we need, the grid still passes the 1 and returns 89 others. There's just no shortage of available electrons. In this case, you get "real trouble" down near 4V on the 6.3V heater. You may have bias-shift at 5V. At 5.9V you will have like 0.050V bias shift, which drifts DC measurements, but just does not upset the audio process.
And as you say: it cools, resistance drops, it sucks more current, doesn't run so cool. Temperature is not exactly regulated but does not wander much. This was key to practical incandescent lamps, except the other way: over-voltage raises resistance and they are not so easily blown as a zero-tempco filament.
What is the complete heat path from one heater to other cathode? The vacuum won't conduct. Leads conduct a little, but any heatsink designer knows you can't push much heat through a wire, you need a slab. Radiation dominates. If you remove all other electrodes, and put your eye on a cathode and look all around, one cathode "sees" 10% other-cathode and 90% non-cathode world. When you put other electrodes back in, exact analysis must be messy, but I think other-cathode heat is a very minor input.
> Just run a tube with heaters only, no B+, they stay very cool.
It varies. 12AX7 phono preamp may have 2 Watts in heaters and 0.1W in plates. His mike-amp is similar except half that power. Turning B+ off won't make them any cooler. OTOH 6V6 Champ Amp has 3W in heaters and 12W in plate; there's little doubt that B+ is (or is not) doing its thing. A heated 6V6 is pretty warm. A powered-up 6V6 is YOW! hot.
