E46 330 belt slip

[Robmilford]

Hi, I noticed earlier this year that the belt driving the alternator, water pump etc was slipping slightly when the car was first started, so I changed it. Now the weather has got cooler again the problem has come back. Last week it was in for a service so I asked for the tensioner pulley to be checked and I was informed that it was ok and some belt conditioner spray was applied. The problem is still there, only on cold starts though. I do need a new battery, it being the original and I was wondering if this was working the alternator extra hard on first start up. Other than this I'm stumped, please help.