2003 Jaguar X-Type Engine Whistle

I have a whistling sound coming from my engine. It only started when the weather got colder. If I warm up the car for about 10 minutes, the noise may or may not appear, but if I don't, it is always there and lasts until the car gets warmed up. When I first drive the car, the whistling noise starts about about 30 mph and the whistle goes up in pitch and then down in pitch as soon as I brake to stop. But if I push on the gas and accelerate fast, the noise goes away. The whistling is usually only there the first time I accelerate and the first time I stop, but then usually goes away, but not always. What do you think the problem is?