Indirectly heated tubes have a reasonable heater thermal mass that tends to reduce thermal shock, the low cold resistance of several parallel heaters tends to load down the transformer secondary at switch-on too at least for the 6.3V ones, rather than the series chain connection 300mA ones. The exception were the 'quick heat' tubes that would flash alarmingly at the termination end.
Particularly Mullard types were/are famous for this; to be clear, it's a normal / intended effect, for parallel operation. Such tubes should not be used in series chains, IIRC.
Most alarming are the directly heated Thorated Tungsten filament tubes, where the filament undergoes a physical transition at ~900k due to the Miller-Larson effect* discovered in 1944. This causes the crystal structure to re-orient as it passes through the transition temperature, leading to necking, cracking and ultimate failure. Although the filaments are rated for around 30k hours, each cycle reduces life by around 0.2%! The only way of mitigating this is to keep the temperature above 900k [Edit: and limiting inrush current to reduce the stress on the increasing number of defects from when you do cycle them]. Not a happy situation for owners of big, expensive, and potentially rare DHTs.
* Morgan Jones, Valve Amplifiers, third edition, pp 261.
Hmm, I'm not aware of any phase change in the W-Th system. Although I don't find a phase diagram offhand, but, it's present in small amounts so is probably either an insoluble impurity or solid solution, and either Th (or ThO2) itself. Pure Th has a phase change (FCC to BCC at 1360°C). Pure W has no phase change, it's the same crystal up to MP. Jones seems to misrepresent this here -- it appears Miller and Larson published in the 50s, regarding creep, not phase change:
https://en.wikipedia.org/wiki/Larson%E2%80%93Miller_relation I don't see anything for either creep or phase transformation for W-Th mixtures, but
https://inis.iaea.org/collection/NCLCollectionStore/_Public/32/053/32053126.pdf?r=1&r=1 is interesting for creep, in the same temperature range, of a couple other alloys. Creep and recrystallization proceed normally at higher temperatures it seems, which is certainly evident in tungsten lamps (especially the blocky recrystallization and sublimation in a failed halogen bulb), but creep should be modestly relevant for thoriated cathodes. (Literal "filament" cathodes, wires and ribbons, are strung up between spring supports, so stress and creep are relevant; very large or specialized transmitters may have self-supporting cathodes, with creep nearly irrelevant?)
I would be inclined to think thermal cycling causes differential stresses, and perhaps activation of grain boundaries/migration (perhaps under electromigration forces too? maybe not with AC though). Maybe that spreads into a stress riser that eventually snaps the filament, maybe it's governed by creep (might the creep timer be reset every time it's cooled down?), no idea.
This probably all isn't too germane for Jones' purposes, more just to say something on the topic, than to give the academic rigor that vacuum tube designers and manufacturers would need, so I suppose it doesn't matter all that much.
Tim