Should I be worried?

A game that have a bunch of characters and stages, not to mention big maps, may require a lot of preload buffering.

I tested something on Pokemon Diamond that actually caused an invisible wall and a game crash by overloading the loading zone sequences on a bike at gear 3 and 4, which I found to be entertaining, but it may theoretically apply to your game as well if it involves memory and buffering.

In maps of such size and detail will have to be loaded in mini-maps, or sectors. Neighboring sectors in view are merely pseudo-loads, or backgrounds. Between the sectors are loading zones to instruct which sector to load and help the game run smoothly. However, the data for the neighboring sectors are preloaded from the disc into memory, and when you cross a loading zone, the system has to update the preload data corresponding with the sector you entered as well as surrounding sectors, requiring that the disc has to be read again at a high rpm rate to make the game run smoothly, lest your game may lag or have the loading screen for each loading zone you cross. The reading rpm may cause slight strain on the hardware as it struggles to keep up with the player's actions and the game's data and speed all at once. The mechanical hum is the disc reader exerting a lot more force than usual to keep the game running smoothly. The vibration from the rapid spinning of the disc reader's motor causes the system to vibrate and induce sound waves in the air that are the hums.

Basically, your 360 is hurting itself from working too hard with reading the disc data, and may need some rest every 30 minutes to make sure the friction of the spinner doesn't heat the system up too much and avoid component damage. It would be different if the game was a download, but this is not the case unfortunately.