**Core Concept**
The concept of increased cardiac output during exercise in a patient with a transplanted heart is crucial for understanding the physiological adaptations of the heart post-transplantation. Cardiac output is the product of heart rate and stroke volume, and in a transplanted heart, the capacity to increase cardiac output during exercise is essential to achieve adequate oxygen delivery to the tissues.

**Why the Correct Answer is Right**
The increase in cardiac output during exercise in a transplanted heart is mainly due to an increase in heart rate, as the transplanted heart is often denervated and lacks the sympathetic nervous system's ability to increase contractility and stroke volume. This is because the transplanted heart is not able to increase its contractility in response to catecholamines, such as adrenaline, which are released during exercise. As a result, the transplanted heart relies on increasing heart rate to compensate for the reduced contractility and maintain adequate cardiac output.

**Why Each Wrong Option is Incorrect**
**Option A:** is incorrect because, while stroke volume may increase in some patients with transplanted hearts, it is not the primary mechanism for increasing cardiac output during exercise.
**Option B:** is incorrect because, although vasodilation does occur during exercise, it is not the primary reason for the increase in cardiac output in a transplanted heart.
**Option C:** is incorrect because, while cardiac contractility may increase in some patients with transplanted hearts, it is not a reliable mechanism for increasing cardiac output during exercise due to the denervation of the transplanted heart.

**Clinical Pearl / High-Yield Fact**
It is essential to remember that patients with transplanted hearts often have a limited capacity to increase cardiac output during exercise, making it crucial to monitor their cardiac function and adjust their exercise regimen accordingly.

**Correct Answer: A. Increase in heart rate.**