There were two important issues with automatic weapons in the Great War; cooling and jamming. While the latter could be cleared reasonably quickly, the former required a timely barrel change. Sustained bursts were asking for trouble because of overheating. An MG08 for example , had at least four spare barrels with each crew. Remember these were the days of corrosive primers; the weapon systems had to be cleaned religously.
Water-cooled MGs such as the Vickers could sustain more and longer bursts than any air-cooled type in land use. I believe the .303 Vickers (water-cooled, variously classified as both "heavy" and "medium") was rated at 10,000 rounds per hour (followed by a barrel change) which would be about a 30% "duty cycle". If I recall correctly the expected proportion of casualties inflicted by the Vickers' was 60% of any double-spaced formation passing across their front at up to 600 yards (2 guns, enfiladed? I no longer recall exactly). Whichever way you cut it, that suggests some sustained firing. Never fired one myself but I seem to recall observing 15-30 round bursts (or more) as being "normal" in engagement, as opposed to shorter bursts for suppression. By comparison, we were trained to operate LMGs in 3-round bursts (that was the Bren and the L2A1 "AR", I suppose it would be the same for the Lewis). Aircraft use would be quite different of course - longer bursts.
Larger calibres handle much greater energies so I expect the .50 and 13mm types (4-5 times the muzzle energy of a "full bore" .30 or 8mm class rifle calibre, as an indication) would not be used so intensively, except in emergency. HMGs are mostly air-cooled these days but not necessarily so back then. Larger barrel = more surface area for radiation, coolant transfer and/or convection but, without the benefit of the calculations, I don't think that would be enough to compensate for additional heat (cyclical rates being "similar"). We have one or two members who are ex-tankers - they would know for sure about their "secondary armaments".
