Another such "reasonable framework" is the orienting response - everything that catches our attention results in a physiological adjustment of the sympathetic/parasympathetic system. So the reasons that feelings feel like something is that the body is responding as a whole. The heart accelerates/decelerates, pupils dilate/contract, etc.
So thoughts can strike feelings (when attended to, we respond with physiological appropriateness so as to be "ready" for what the thought imply). And perceptions also demand some constant adjustment of the state of the body.
The explanation gets more complicated with motivating drives like thirst, hunger, sex. But this is a form of perception and attention too. When our body dries out, this is mapped as a sensation to the brain and so drives a response.
The mapping of internal sensation is hierarchical and complex just as it is with any external sensation. So the hypothalamus might be signalling "thirst" while the orbital prefrontal and cingulate cortex are saying "shut-up", we've got more important things on our mind right now.
So short answer is that emotion/feelings are part of cognition generally. There is a natural need to keep the body in the right mood, the right set-up, to match the demands of the world. This is happening both in a constant fine-grained way (the orienting response) and in a more dramatic, long term fashion (drives and their satisfaction).
On top of this, humans have socially constructed emotions - google Rom Harre as the central figure in that field.