Recently also bought a 1970 Fiat 500L which required a bit of work.
On return from the garage found that once warmed up the Car would not restart. Did find that although the coil (spark plugs, leads and condenser) had been changed, the coil was getting hot. Waited a while, until the coil seemed to be cooler and then successfully restarted. Assumed the coil would need to be changed again.
Changed the coil for a new one, however this did not solve the problem.
A change of points (should have done this when the plugs, etc were changed but had no feeler gauges so had left this item) and re-adjustment of the tappets and so far the problem seems to have gone away.
