Sounds like the regulator rectifier part of the alt is suspect, a recon is about £50.
I would first make sure the inside of the blue wire connector on the alt is nice and clean.
Problems like this are classic of a breaking down alt, reg/rec, these do as said above contain diodes(one way electrical valves) used to convert ac to dc, + regulator part controls the current.
I've had one expire on the rollers before now when it got too hot, the solder melted!!
tabetha