Is it possible to improve interoceptive awareness/accuracy? If so, how? For those unfamiliar, interoceptive awareness/accuracy involves awareness of, and sensitivity to, internal physiological sensations ("My heart is beating fast").  Interoceptive information is fundamental to how we conceptualize our affective experiences. For instance, people with high interoceptive sensitivity may be more likely to emphasize information about high/low arousal in their emotional self-reports (Barrett, Quigley, Bliss-Moreau, &amp; Aronson, 2004).  Sensitivity and awareness of interoceptive information is fundamental to many other forms of cognition as well.

My question is whether we can improve people's interceptive awareness/accuracy with some sort of intervention (e.g., biofeedback) and whether this improvement might predict other adaptive outcomes.
Interoceptive awareness and accuracy
Interoceptive awareness and accuracy are sometimes used interchangeably, but can also refer to two different things: awareness to the tendency to attend to interoception measured by self-report, and accuracy to the actual accuracy with which one does so (Chentsova-Dutton and Dzokoto, 2014). For example, a cross-cultural study involving West African and European-American found that &quot;West Africans showed higher levels of interoceptive awareness, but lower levels of interoceptive accuracy than European Americans&quot; (Ceunen, Van Diest and Vlaeyen, 2013).
Heartbeat perception training
There have been some recent attempts to produce improvements in interoceptive awareness and accuracy. Schaefer, Egloff, Gerlach and Witthöft (2014) gave 29 patients with somatoform disorders heartbeat perception training, and reported that the training selectively improved interoceptive accuracy in patients with low health anxiety, as well as improvements in symptoms.
Mindfulness
Silverstein, Brown, Roth and Britton (2011) also found that mindfulness training produced a statistically significant benefit in speed of interoceptive awareness, and that this improvement was associated with improvements in attentional, self-judgmental, and clinical factors of female sexual dysfunction. They reported the following about increased interoceptive awareness:

Women who participated in the meditation training became significantly faster at registering their physiological responses (interoceptive awareness) to sexual stimuli compared with active controls (F(1,28) = 5.45, p = .03, $η_{p}^2$ = 0.15).

Another recent study of experienced meditation practitioners did not report a benefit of meditation on either interoceptive awareness or accuracy, however (Khalsa et al., 2008). Additionally, I am generally skeptical of the benefits of mindfulness on cognitive ability. See Jeromy's answer about the general effect of mindfulness on cognition.
References

Ceunen, E., Van Diest, I., &amp; Vlaeyen, J. (2013). Accuracy and awareness of perception: related, yet distinct (commentary on Herbert et al., 2012). Biological psychology, 92(2), 423-427.
Chentsova-Dutton, Y. E., &amp; Dzokoto, V. (2014). Listen to your heart: The cultural shaping of interoceptive awareness and accuracy. Emotion, 14(4), 666.
Khalsa, S. S., Rudrauf, D., Damasio, A. R., Davidson, R. J., Lutz, A., &amp; Tranel, D. (2008). Interoceptive awareness in experienced meditators. Psychophysiology, 45(4), 671-677.
Schaefer, M., Egloff, B., Gerlach, A. L., &amp; Witthöft, M. (2014). Improving heartbeat perception in patients with medically unexplained symptoms reduces symptom distress. Biological psychology, 101, 69-76.
Silverstein, R. G., Brown, A. C. H., Roth, H. D., &amp; Britton, W. B. (2011). Effects of mindfulness training on body awareness to sexual stimuli: implications for female sexual dysfunction. Psychosomatic medicine, 73(9), 817.