J68

I have a problem with a 1998 LS400 - its has been off the road for a while as the alternator had failed. This has now been replaced and appears to be working fine when the car starts. The car runs for around 10 minutes and then cuts out - the battery voltage drops just before cut out from initially around 14.6v to less than 13v. The car will not then restart until it has cooled down completely. Has anyone had any similar issues?