If you can make it through the training, then you already know how stressful this job can be. Your early career will test your knowledge constantly, and you'll be asked to do your work as quickly as possible. The average work week for a resident is fifty-one hours—which isn't too bad until you realize that much of that comes in the form of eighteen-hour shifts.
The stress doesn't end once you become a full-fledged radiologist. You'll have to identify and treat diseases using technology that's changing all the time and that can be risky to work with. And because you're dealing with deadly diseases, you really need to be right when you make your diagnoses. Misdiagnosing not only hurts the patient, it costs the healthcare industry billions of dollars.
Basically, if you can perform at a superhuman level at a superhuman speed, without freaking out, you'll be fine. Pretty big "if," but that's why you get paid the big bucks, right?