Technically speaking, any card in the deck can refer to health and illness, it all depends on the context and the question asked. The four suits can certainly indicate different types of health - mental, emotional, physical, spiritual etc. As for the Sun card, many would probably see it as a good health card in general. However, it could also be referencing a fever, or the risk of dehydration. It all depends!

I have seen The Star upright indicating a return to good health. (In fact that has happened to me personally.) Also Strength upright but that usually implies an ongoing situation, in which perseverance and calmness creates a desirable result. Actually there are lots of cards that can give information about health issues—including those already mentioned on this thread—but I suspect they need a question regarding health in order to be obvious. I don't think there are many cards that automatically mean 'health' ...either good or bad health. Context is key. This is why I'm not a huge fan of card reading 'blind,' without any indication of what the querent is concerned about. I'm not psychic. I need context in order to read accurately.

Not sure if it is strictly meeting your criteria, and a little too specific: 3 of Swords: surgery (any sort that involves cutting into the body in any way) or heart disease and cardio pulmonary issues (Swords being air/oxygen delivery/lungs - and of course the pierced heart in the RWS image). Pentacles as the physical body/material conditions would be a good indicator of what is happening in that direction. King of Pentacles: hospital; medical specialists. Page of Pentacles: news about health/test results. But as you asked - Health: Sun fits as it is giver of life and vitalising. Depending on whether there's excess or insufficiency around it. Temperance may mean homeostasis - either in, returning to, or away from. Maybe also Ace of Pentacles as it represents a sort of wholeness - a sort of virginality of the body before our life choices, consumption and environment has its way. Illness: 5 Pentacles.