Rand, alas, never provided any evidence for this assertion. Her chief disciple, Leonard Peikoff, did provide the following:
...When, as a college teacher, I would reach the topic of emotions in class, my standard procedure was to open the desk, take out a stack of examination booklets, and, without any explanations, start distributing them. Consternation invariably broke loose, with cries such as "You never said we were having a test today!" and "It isn't fair!" Whereupon I would take back the booklets and ask: "How many can explain the emotion that just swept over you? Is it an inexplicable primary, a quirk of your glands, a message from God or the id?" The answer was obvious. The booklets, to most of them, meant failure on an exam, a lower grade in the course, a blot on their transcript, i.e., bad news. On this one example, even the dullest students grasped with alacrity that emotions do have causes and that their causes are the things men think. (The auditors in the room, who do not write exams, remained calm during this experiment. To them, the surprise involved no negative value-judgment.)...
There are at least two problems with this: first, it's merely an anecdote and as such cannot be regarded as decisive on this issue; but even more critically, the anecdote doesn't establish what it claims. Even if "the dullest students grasped with alacrity that emotions" are caused by "the things men think," the reactions to the surprise exam don't establish this. Peikoff's anecdote begs the question. For the real question is not whether emotions are inexplicable or whether thinking may influence emotions, it's whether emotions are entirely the product of thinking. The Objectivist claim is that the value judgment comes first in the form of a conscious thought, and the emotion comes afterwards. But it's quite possible (and, indeed, far more consistent with the obvious evidence) that the causation is, at least in some instances, reversed: that is, that value judgment could not have taken place without a prior emotion.
Evidence for the emotion-must-comes-first view can be gleaned from many sources. Indeed, it would appear to be a fairly obvious inference from facts commonly known. Consider the following from the Aristotelian scholar Neera K. Badhwar:
The idea that the emotions have to be programmed by the intellect, whereas the intellect can choose values independently of any help from the emotions, suggests a hierarchical relationship between intellect and emotion, and a unidirectional picture of moral and psychological development. First the intellect, functioning independently of the emotional faculty, collects the data and makes value-judgments; then it programs the emotional faculty. On this picture, the preprogrammed emotional faculty is inert, unable to make any value responses, and unable to play a fundamental role in forming or aiding the intellect. [Note: Badhwar provides evidence for this view in her footnotes.]
However, if infants and young children (not to mention animals) have emotions in a pre-conceptual form -- as they surely do -- then emotions cannot be entirely dependent on the intellect. We feel fear, anger, contentment, empathy, and pleasure in a pre-conceptual form long before we acquire the capacity tomake value-judgements. Insofar as these are responses to that which we sense as somehow good or bad for us, valuable or disvaluable, it follows that we are able to make value responses long before we are able to make value-judgements. Indeed, it is only because we have this pre-conceptual ability for responding to value that we can acquire the capacity for making value-judgments. Thus, preconceptual emotions are necessary for having any more than the most primitive values in the first place, and, thereby, for making value-judgments. Adult emotions build on these pre-conceptual emotions and the value-judgments they make possible. For example, adult fear typically contains not only the components of feeling and physiological response that a child's fear does, but also the value-judgment of the feared object as dangerous or threatening. Which objects are seen as fearful depends not on the judgments of an untouched intellect, but an intellect already shaped to some extent by our preconceptual emotions, and continually influenced by, even as it in turn influences, our adult emotions.
Some Objectivists have claimed that evidence on behalf of Rand's theory of emotions has been compiled on behalf of cognitive behavior therapy (CBT). The assumption is that CBT=Objectivist theory of emotion. There is no reason to believe this. One of the originators and most influential advocates of CBT, Albert Ellis, wrote the first critical book on Objectivism (Is Objectivism a Religion?), and he made it quite clear that Rand's theory of emotions was simplistic and inadequate:
The virtually perfect, one-to-one relationship between our thought and emotions that Rand and Branden posit is practically nonexistent. Consequently, if they wish to remain unchallenged, their position had better be modified. An emotion tends to arise from a value response. It usually is something of an automatic psychological result of our value judgments. It has, however, other important causative factors connected with human sensing, perceiving, and acting.