I absolutely expect helium drives to run cooler simply because helium is a much better conductor of heat compared to air. As a result all heat generated in the drive cavity will be more effectively conducted to the containment vessel and leave the material inside consistently cooler.

Unfortunately air is an excellent insulator. I looked it up and helium has thermal conductivity and heat capacity about 5 times higher than air.

So significantly better but we have to remember that solids have something like a thousand times better thermal properties than gases and it is the solid bits we are mostly concerned with. So it really depends on where the heat is originating in the drive. I suspect the big advantage is the lower viscosity of helium which prevents heat generation in the drive cavity in the first place.

That's a two way street though. If the ambient is higher it will carry the heat from the outside into places in the drive where it can do real damage.

For an excessively hot exterior sure, but I was thinking back to an experience at NetApp when thermal inside was the issue. When NetApp first started using SATA drives (rather than Fiber Channel) in their Nearstore appliance we discovered that the SATA drives were negatively effected by writing too much. Specifically, if write duty cycle was too high, the r/w head got too hot, and the heat caused it to change shape slightly and that shape change caused it to fly higher. Leading to something that was dubbed 'high fly writes' which splattered into adjacent tracks and could corrupt data. One fix was to keep track of the write duty cycle and to let the drive 'rest' for a bit to keep the overall duty cycle into something the drive could handle.

I don't think that sort of failure can happen on a helium drive.

You're right about that, in a drive filled with helium inside the drive the temperature gradients will be flatter.

Heat transfer in computing hardware is a super interesting subject.

The drive produces heat, so it will always be hotter than ambient (proportional to the heat generated times the thermal resistance).

Not necessarily, the drive produces heat but something around it (other drives, cpu's) may be producing a lot more heat than the drive raising the temperature of the drive casing beyond where it would be if it were just the drive in isolation.

Case design for lots of drives + a beefy CPU is very tricky if you want to really balance the airflow so that there are no large local variations in temperature.