I don't know much about this, but my understanding is that a hot core is not itself something that life particularly needs. The effects of that hot core however (Spinning core to make a magnetosphere? Volcanic activity changing atmospheric chemistry?) are probably more important.

On the other hand, a hot core gives you deep sea thermal vents. Although I think the current prevailing theories don't have life originating near those on Earth, a hot core is certainly essential to life down there and, perhaps on another world, life could originate there.