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My instinct tells me that shouldn't be a problem. The grid goes at most 10-20 volts positive with respect to the cathode (I think it is in fact only a few volts because of the cathode resistor), so the power dissipated in the grid will be tiny. Probably gets way more heat from the nearby cathode than from the actual power dissipated in the grid. I was more worried about whether this will cause some kind of cathode stripping or something like that.
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