something to try is turn the console off, then check all point of the power cable. blow dry then hover the vents on the power brick to remove all the dust. worked for me. just try and keep the brick well ventilated. also try blow drying and hovering the console just to be safe
My sons Xbox kept making this weird noise while he was playing it was driving me mad someone said it was dust on the fan so while he was out I cleaned it I got the hoover and hoovered any where I could see that there was and vent leading inside the Xbox and it worked for a short while so now every time I hoover up I go over the Xbox and since I’ve been doing that no whistling thank god because it was driving me mad
I fixed mine (so far at least) by taking canned air and blowing out all of the built-up dust on the heat sync. I would also recommend doing this to the power supply and the kinect if you have one. But make sure the Xbox is turned off, doesn't matter how from what I've found, it's just the fan can’t already be spinning.