My generator light illuminates but only after a few minutes of running the engine. The first time I noticed it was when I was driving, the gen light started to flicker, continued driving till the light becomes constantly illuminated. So, I thought alternator or regulator may be going bad. The next morning, I started the car, the gen light does not illuminate anymore. Drove the car around the block, then gen light starts to illuminate again. I am suspecting that it had something to do with the engine temp rising. Probably a wire associated with the charging system is heating up and causing the generator light to come on. What would it be? Your advice is highly appreciated. Thanks.

Some follow up info... I recently had the starter replaced. Before this, the gen light was not illuminating except when turning ignition on.