The recoil becomes exaggerated, not due to the fouling but because the constant action on the shoulder will in time cause a bruise to develop. It will get progressively worse, especially if the rifle is not held properly. If you pick up a rifle that has fired say 30 rounds, but you haven't fired any, it is just the same as it is firing from cold, but the previous shooter will comment on its recoil.
Firing prone, if you are not fully supported on your elbows will cause the butt plate to sit on the top of your shoulder, not the fleshy part at the front, it does exaggerate the recoil, as the impact has to be absorbed throughout your body, rather than firing from the knee or standing where you can follow through with the recoil and move back with it, similar to the arrester springs do on an artillery piece.
You are more accurate though firing prone.
The Martini Mk2 bullet was wrapped in cotton fibre paper, dipped in beeswax and pushed through a heated die. A wax concave plug was fitted behind it, the idea is three fold: to scrub the bore, leaving a lubricant behind it after each round, to prevent Metal/lead contact in the bore, So hypothetically the only fouling is that from the last shot. As it gets hot, (its not that bad,even after 40 rounds, in less than an hour, my normal Sunday) the wax plug atomises and lubricates. In Zululand, where the atmosphere is very damp indeed, it will help in turning the foul to a liquid, the old soldiers would blow down the barrel to keep it topped up from the moisture in the breath.
In the Mk3 Martini cartridge, the beeswax plug had a hollow concave to the top, it was found in earlier rounds, in cold conditions, the wax simply followed the bullet down the barrel, and did not do anything. So, the air gap forced open the wax outwards so it ensured lubrication. (take a tomato, halve it, scoop out the middle, lie it flat on a chopping block an splat it flat.it spreads out,).
In conclusion: is the recoil worse, physically no. mentally yes.
Does the barrel get hot, yes, depending on the firing rate, but with the average expenditure of 33 rounds per man over an engagement, not that bad. The men did fashion cowhide wraps, so it stopped any discomfort. it became a standard item on kit in 1883.
here is a report from 1875, I have just bullet pointed it
Col H.C Fletcher 2nd Bttn Scots Fusilier Guards
Rifle No 87 & 647 fired over four days without cleaning.
400 Rounds fired, Two handfuls’ of dry sand poured in action & three rounds fire with no problems.
2 rifles buried in Snow, sand and earth, again 10 rounds fired and worked perfectly.
50 rounds fired with great rapidity, had become extremely hot “some extraction difficulties”, but on cooling the rifles worked well.