Bulging disc. my hands feel warm water as not warm enough, my feet as too warm, and my body between. is it nerve damage?

Hard to say: If the disc is just bulging and not compressing the nerve roots, it is unlikely to be the cause of symptoms and unlikely to cause nerve damage. Also if the bulging disc is in the lower back, you will have symptoms in the leg and feet rather than the arms and hands. A neuropathy is a different problem that is not related to the disc. This is from irritation of the nerves by a systemic process.