The particular sensation of "the feeling of warmth in my chest" is already being investigated by psychological researchers. They refer to it as “elevation”. This is what they have to say about it: Elevation appears to be the opposite of social disgust. It is triggered by witnessing acts of human moral beauty or virtue. Elevation involves a warm or glowing feeling in the chest, and it makes people want to become morally better themselves. Because elevation increases one's desire to affiliate with and help others, it provides a clear illustration of B. L. Fredrickson's broaden-and-build model of the positive emotions.
Here are a few quotes and links.
http://www.naturalism.org/naturali.htm
The spiritual experience - the experience of meaning, connection and joy, often informed by philosophy or religion - is, from a naturalistic perspective, a state of the physical person, not evidence for a higher realm or non-physical essence. Nevertheless, this understanding of spirituality doesn’t lessen the attraction of such an experience, or its value for the naturalist. We naturally crave such feelings and so will seek the means to achieve them consistent with our philosophy.
http://www.naturalism.org/spiritua.htm
Although naturalism may at first seem an unlikely basis for spirituality, a naturalistic vision of ourselves and the world can inspire and inform spiritual experience. Naturalism understands such experience as psychological states constituted by the activity of our brains, but this doesn't lessen the appeal of such experience, or render it less profound. Appreciating the fact of our complete inclusion in nature can generate feelings of connection and meaning that rival those offered by traditional religions, and those feelings reflect the empirical reality of our being at home in the cosmos.
http://www.naturalism.org/spiritua1.htm
If you look up the etymology of the word "spiritual," you’ll find that it derives from the Latin "spiritus," meaning "wind" or "breath." Standard dictionary definitions of spiritual contrast it with physical or material, so dualism is more or less built into the ordinary conception of spirituality. But I will argue that just as we can be good without God, we can have spirituality without spirits. Even within the monistic view of the cosmos entailed by a commitment to scientific empiricism, we can avail ourselves of spiritual experience and take an authentically spiritual stance when appreciating our situation as fully physical creatures embedded in a material universe. I hope to show that in its dualism, the traditional notion of spirituality in effect sets up problems of existential alienation and cognitive dissonance that religions have wrestled with, more or less unsuccessfully, for millennia. At a stroke, naturalism cuts these problems off at the root, providing an emotionally satisfying and cognitively unified basis for feeling completely at home in the world.
Psychologists are also studying the emotion of awe. "Awe is a distinct emotion, and specifically an aesthetic emotion (Loew, 1997). And though it might seem that awe is more likely the result of positive stimuli such as a sunrise at sea, rather than the result of negative stimuli such as a tsunami wave, awe does in fact occur in the face of both pleasant and ominous stimuli. Dangerous stimuli such as volcanic eruptions, battles, or extreme electrical storms can produce awe. However, the experience of awe cannot occur if the percipient is in actual danger. A direct threat of harm produces an emotional response of fear, overriding awe. To experience awe rather than dread in the face of forbidding stimuli, one needs to be an observer at safe remove."
As far as we can tell, all mental representations, sensations, perceptions, and emotional states are produced by neurons. During brain surgery, the doctor often electrically stimulates various neurons around a tumor to determine which neurons to cut around. While doing this, the patient is awake and will report seeing lights, hearing sounds, thinking of words, or tingling of limbs. The limbic system, which is responsible for the experience of emotions is deeper in the brain and so is not usually stimulated this way during surgery. However, through drugs and other means, researchers have been able to reproduce many of the sensations involved when having a spiritual experience or near-death experiences. For just a taste of the exciting research in this field
See http://www.maps.org/media/vedantam.html