What I find interesting is that while we truly can experience physical sensations associated with certain thoughts and parts of our body, we can also manufacture the same (or even stronger) sensations by force of will and belief. If we want something to occur badly enough, we're able to "think ourselves" into having that experience. Likewise, if we have some established beliefs and expectations regarding the experience, we may be able to create an experience far more dramatic than the reality.
For example, I smoke cannabis to meditate on ideas as part of my creative process. If I smoke and try to slack off, try to relax or let the TV do the thinking, I get a strong physical reaction. I get heart palpitations, my hands shake, I get lightheaded. When I spend time talking ideas out with other people or working on them alone, these symptoms disappear. They seem to be a very obvious physical reaction to my activities being out of sync with my state of mind. I always try to remind myself that there's no way of knowing why this happens. Does it happen because I imagine it or does it happen because there's some objective truth behind it? Maybe it's psychosomatic. In the end with things like this, whatever you believe becomes the truth. You think it's a figment of your imagination? Then it may as well be. You think it's some greater force? So it is.
The trembling of fear, the chill of regret, a rage that makes you shake...real or not, we all experience physical sensations accompanying our thoughts. Personally, I think we are part of an unfathomable soup of fundamental particles made from some type of universal energetic substrate. Elaborate and beautiful as our tapestry of the physical universe may be, it is all woven from the same thread. Why shouldn't we expect to have some sense of electrical kinesthesia with our own bodies and the world around us, being so fundamentally comprised of the same primary substance? Even "empty air" is full of the same particles as everything else, all of it the manipulation of a more elemental field of energy. Some even theorize that everything we call "physical" is actually a hologram. It's easy for us to get carried away with our assumptions and conclusions and what-ifs, but there's no denying the bare fact - everything is energy.
As such, we are constantly being bombarded with all kinds of this wave energy, all of varying substance and effect, many on levels imperceptible to us. Our bodies are constantly absorbing radiation and electromagnetic waves from the world around us. Some of it can heal us and some of it can connect us and some of it can kill us. Just as a fish would be blind to water - the primary element of its habitat - we aren't always conscious of our charged, oscillating atmosphere. We don't always consider that thoughts are electromagnetic waves that originate within our skulls and travel outward into the world. If our thinking brain emits this energy into the wider world of waves, why shouldn't we expect those waves of mental energy to interact with and influence the body that created them? Even barring that physical interaction, our conscious experience of physical sensations is a construct of our own minds, a mental object. It's no stretch at all to suggest that our thoughts could influence our perception of what it "feels" like to be conscious at any given moment.
tl;dr I think it's highly likely we may experience chills, twitches, vibrations, shudders, or any number of other physical reactions in line with our state of consciousness.