Why do my feet burn when I put them in bath water and the water isnt hot to the rest of my body?

Burning Feet. Burning feet can occur simply because your feet are tired. Athlete's foot can cause burning feet. Burning feet can also be a symptom of nerve damage (peripheral neuropathy), perhaps due to diabetes, exposure to certain toxins, chronic alcohol use, certain b vitamin deficiencies or hiv. See your doctor for an evaluation.
Weird foot sensation. A good likelihood is that you may be experiencing some initial symptoms of diabetic neuropathy. This can lead to weird altered sensations such as burning, tingling, and even increased warmth. By controlling your blood sugar this can curb some of these weird sensations. Also some of your medications may add to some weird sensations as well.