It could be many things, unfortunately and without hearing the noise first hand or being able to do some basic diagnostic tests or be able to drive the car, its hard to say what the source of the noise may be. I would say power steering oil being thick and as it warms up the noise may go away or engine oil being to thick (wrong viscosity). Is it still under warranty or extended warranty? Get a professional opinion you may want to drop off your car the night before so the engine and oils are cold so that the person working on your car can experience the noise.
Noises are a difficult concern to address, especially with out hearing the noise. I would recommend bringing the vehicle in, as it may be a normal noise. ( We would be able to show you others, if this is the case) Ususally engines make different noises when cold vs hot, caused by expansion of the parts inside, and clearences cold vs hot. we would be happy to listen to your noise Monday through Friday, Saturdays are very busy and the wait time usually doubles.
Regards,
Billy Stewart
Longo Toyota
