You can step into a yoga class looking for an exercise, because the doctor told you it's good for some kind of pain or to strengthen your core and fix your posture. You can be trying to improve your concentration, relief stress, have some "me time" and relax. Or you can be following a spiritual path, looking for a deeper body/mind/spirit connection.
There's no right or wrong reason when it comes to yoga; the perfect one is the one that fits you and gets you there. You're not closer to getting enlightened if you're following a spiritual path, and you're not shallow or a "bad yogi" if you just want to nail a handstand and flatten your tummy. Take what works for you, and leave the rest. For me, it was the physical stuff that got me there. I wasn't ready to look deeper within me at that time. But hey, it got me there!
The yogic philosophy describes three levels of human embodiment; a causal body made up of thoughts and beliefs, an astral body of emotions and desires, and a physical body composed of the material substance.
The beauty about yoga, is that no matter what your first motivation was, you'll get a taste of all the aspects it has to offer. You will get stronger and healthier from the physical practice. Your concentration and the awareness of your body will improve. You will start to notice the effects some food, people or events have on you. And, at least during Savasana, you will enjoy the benefits of being relaxed and feeling connected to something greater (and maybe divine).
Too much yoga can make you HOT, because it will show on your healthier body, an ease and calm mind, and a softer spirit and there's no way of hiding it. But how does this work if I'm only showing up to exercise? A brief explanation is found below.
The Ashtanga Yoga system, also found in the Yoga Sutras of Patanjali, describes an eight-stage process to achieve a higher level of integration.
(1.) Yamas (don'ts -i.e non-violence, truthfulness, non-stealing) and (2.) Niyamas (do's -i.e purification, contentment, self-discipline) where a set of actions you should and shouldn't do are described. This is a moral training to try to dominate both conscious and unconscious elements of the mind, so one does not become a selfish, antisocial individual.
Then we have the (3.) Asanas (physical postures) and (4.) Pranayama (regulation of the breath). This two practices help us achieve a regulation of vital energy, blood circulation, and nervous and muscle functions. The physical postures help us get in shape, the breath control is linked to the control of the operations of the heart and the autonomic nervous system. Both of which are a bodily/physical training.
(5.) Pratyahara (withdrawal of the senses; where you direct your attention to one specific point of concentration, and reduce the distraction from the senses), (6.) Dharana (concentration that is achieved holding that focus in one single point), (7.) Dhyana (meditation, where the concentration increases for longer periods of time), and (8.) Samadhi (sense of oneness, when the object of our concentration is achieved, everything is engaged and connected). This four stages are part of a spiritual training. The mind responds to the outside world information it receives from the senses, distracting it from its "true nature". This steps are designed to work towards a higher dimension, where there is no restriction from the ego or physical limitations.
Don't worry about being a "good yogi" or "bad yogi", there's no such thing. Just show up on your mat and do your best. Even if for theoretical purposes our three bodies are explained separately, we are one. And when we start working on one, we are also opening the doors to work on the others two.