My husband's tsh level is below 0.01 also he has fever since 1 1/2 months he wakes up suddenly fromsleep with high heart rate is his condition serious?

Yes: He may have thyrotoxicosis -- bring him to er now.

Maybe: Awakening with a feeling of palpitations is fairly common, and may result simply from a dream or a rush of adrenalin. Also, having a low TSH may not be pathologic if the active thyroid hormones are normal. However, if your husband has hyperthyroidism, and these symptoms are from that, then he has a serious condition which requires medical management.