Even if he bullet doesn't melt it would foul the barrel right quick wouldn't it? 2000fps with a gas check maybe
Lead fouling in a barrel can be caused by several factors.
-undersized bullet
-rough or uneven surface inside the barrel
-no lube or wrong lube for given velocity
-excessive pressure without a gas check (past about 1700fps you want a gas check but it is different from barrel to barrel)
-other stuff I'm forgetting
Generally you want to use a cast bullet that is at least 0.001" over bore diameter (you have to slug your bore) but I have used bullets up to 0.005" over without issue. You have to use an appropriate lube for the velocities you are pushing the bullets to, gas check if necessary, and use a hard enough lead alloy for your purposes.
The hardness of lead alloy can be controlled through several means but some are only temporary. Pure lead can be water dropped (quenched) to harden it but it will soften in a matter of hours. Lead-tin alloy is harder but can be made even harder with water dropping. The lead-tin alloy will soften back to it's non-quenched hardness (which is still harder than pure lead) after a few weeks though. Another significant advantage of tin in the alloy is it allows the molten metal to flow better so you get fewer bad bullets (gaps, bubbles, etc.) when casting. Lead-antimony or lead-tin-antimony alloy is even harder but has the same effect of quenching and softening again over time. The hardest lead alloys are lead-tin-antimony-arsenic; it again will soften over time if quenched but the point it will soften to is still quite hard.
People push gas checked, hard alloy, cast bullets with the proper lube to 2500fps and beyond without leading or significant fouling. It's far more complex with more variables than shooting jacketed bullets but most people who shoot cast tend to be tinkerers anyway.