We give a new simple proof of the time hierarchy theorem for heuristic BPP originally proved by Fortnow and Santhanam [FS04] and then simplified and improved by Pervyshev [P07]. In the proof we use a hierarchy theorem for sampling distributions recently proved by Watson [W13]. As a byproduct we get that P is not included in BPTime[$n^k$] if one way functions exist. As far as we know this statement was not known before.
We also show that our technique may be extended for time hierarchies in some other heuristic classes.