From a point of view like that of theories of emotion like those of James and Lange, especially as elaborated in Antonio Damasio's somatic marker theory, it is more likely that a thought is sandwiched between the two halves of every emotion.
In those theories, emotions arise physiologically before the thoughts associated with them, but they are then evaluated in terms of experience before becoming actual feelings. That evaluation is a thought, one way or the other, even if it is often fleeting or unconscious.
The same physiological reaction might become fear, exhilaration, anger or passion, depending on the thought that shapes it. But the thought would not occur unless some emotion were already in the process of arising.
Damasio's evidence for this is that he observes those deprived of emotional reactions by brain damage often lose the ability to apply logic to everyday situations, even if their actual logic is unimpaired. His theory is that without the incipient emotion, logic often does not kick in and do its job of helping us make decisions.
For your example of cold, your body might actually start preparing to shiver, or raise gooseflesh to conserve body heat. Then your mind might have to decide whether it is cold, scared, or filled with anticipation before you actually feel cold. If you decide you are not actually cold, that incipient shiver might be transformed into something quite different, like a lurch out of the way, or a laugh.