I usually tin the cable, wait for it to cool and then use some sort of "demel tool" and use the tool that can "sand/grind" metall in order to remove just a little bit around the tin cable to make it fit.
I make sure to remove the same on all sides (the cable is round, the tin around the cable is round, make sure to grind it round). It will fit perfectly after couple of minutes of work...
You can do the same with batteries which usually also have thick wires.
Sorry if some words perhaps are not correct, I'm not sure what its called in english when you "sand" or "grind" or whatever its called...
But the below pic should explain which tool I mean...

Its the brown flat and round part in the middle...
By the way, what is that called in english? Do you grind?
