If an ex of a partner you've been dating for a couple of months warned you that they were a cheater. Of course it would be more believable from someone else other than the ex but how would you react if it was the ex. Would you believe them or not?
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I'd ask myself what motivation they would have to lie. Aside from pure spite, they have nothing to gain, do they?
So I'd ask your current flame about the ex...you don't need to repeat what he said, just that you had contact with the ex. Watch their eyes, carefully, and see if they seem troubled. Or angry. You can tell a lot by how they react.
Also you could ask the ex exactly how the ex knows they are a cheater. See if he/she can readily give the time and place and cite exactly what happened.
I wouldn't dismiss the accusation without trying to see if their statement 'rings true.'