Unexplained Fever , Heart Palpitations

I am a 26 year old female, 5 foot 3, and weigh around 95 pounds. People say I'm thin. I am not losing any weight - I have been around 95 pounds since I was 20. My work (I am a developer and systems analyst) involves sitting in front of my laptop for hours (sometimes more than 10), lots of mental work. Sometimes I do not sleep till early morning, and then get up in the afternoons. Sleep comes very easily to me. I always have a slight constipation. I cannot stand cold temperatures - I bathe with lukewarm water even in hot weather. My blood pressure is almost always at the lower side (90 systolic, 60 diastolic).

Here is my problem:

For the past one year or so, I have had low-grade fever (98.8 - 99.5 F) which occurs ONLY in the evenings - after sunset till midnight. This is accompanied with a slight burning of the eyes - that is how I know the fever has started. Sometimes I feel cramps and body discomfort. I cannot work or do anything during that time. I get palpitations when I lie down. This is started to increase lately.

1. My doctor had a chest x-ray taken, which came out to be normal. She was looking for any signs of tuberclosis (latent?). She said I was anaemic and gave me some iron and multivitamins.

2. She also had a blood ESR (erythrocyte sedimentation rate) test taken. I had 2 tests taken from different labs, with a month in between. The values were 5 mm/hr (0-20 normal) the first time, and 13mm/1st hour (0-15 normal) the second time.

3. Had an ultrasound of the stomach and the pelvic area, which also came up fine.

4. The doctor also recommended a thyroid test. Here were the values:

TSH: 1.25 mU/L [0.4 - 4.5]
Free T3: 182 pg/dL [230 - 420 pg/dL]
Free T4: 1.25 ng/dL [0.8 - 1.5 ng/dL]

As you can see, my FT3 is way below normal.

The doctor says all is well and that such a light fever is nothing to worry about. But I feel SICK. And that's a problem for me.

After a lot of reading all over the Internet, I think I might have HYPOthyroidism. But I have no hint of weight gain. In fact, I can eat as much as I want and I never gain anything. I'm really confused and just want to get rid of this fever and palpitations. Please help. Thanks in advance.