First of all, it is impossible to determine the exact mechanism of how thalassemia causes fatigue in the human body. There are just so much that we do not understand, and it will differ from various individuals as well. The only thing we can do is take some supplements and implement lifestyle changes in terms of the foods we eat and exercise properly to accommodate our condition.
I too have beta thalassemia minor like you, and have researched a bit on how to deal with it. Looking at the bright side, you have to realize that our thalassemic condition was actually meant to be a defense mechanism against malaria. Normally, people with beta thalassemia minor don't experience symptoms. That was the case with me as a child, I was perfectly healthy and active, but as I grew older bad nutrition and poor exercise habits caused some symptoms like fatigue to manifest.
I have compiled some supplement advice from Andy posted in the supplement section:
http://i.imgur.com/N4ICU.png There are 2 promising drug trials currently in development, the HQK-1001 and ACE 536 for beta thalassemia.
The fatigue from the slight anemia was significantly reduced after I took supplements and followed a paleo diet. It is important not to consume processed foods or wholegrains/milk/rice/beans that contains chemicals like Leptin and Gluten that causes gut irritation. When your stomach cannot digest and absorb nutrients properly, you'll feel fatigued more easily.
http://www.fourhourworkweek.com/blog/2010/09/19/paleo-diet-solution/You can also incorporate more spicy foods that contain curcumin in your diet, as research shows that it improves the oxidative stress in beta-thalassemic individuals.
http://www.ncbi.nlm.nih.gov/pubmed/19900435Then there's the standard drinking of water daily, as that will help cleanse your system and stimulate blood cell turnover rates. Green tea will also help as a powerful anti-oxidant.
Look up a list of super foods like blueberries that are powerful anti-oxidants and incorporate them into your diet.
Vitamin D levels are also very important.
http://jackkruse.com/the-sunshine-of-your-life/I checked my vitamin D levels and had 27.3, and the optimal levels are around 50. So I've been taking liquid vitamin D supplements of at least 5000IU every day, and will be rechecking my levels soon.
As for exercise, since our gene defects affects the production of beta globin proteins which results in excessive destruction of red blood cells, we need to reproduce them more rapidly. The process is called Erythropoiesis, which is regulated by the hormone erythropoietin. About 2.4 million new erythrocytes are produced per second for a normal person, the number is probably higher for us. There are some supplements that could help boost erythropoietin, click on this link:
http://i.imgur.com/VZJrc.pngTestosterone is known to boost erythropoiesis and hemoglobin production as well.
http://www.ncbi.nlm.nih.gov/pubmed/18160461 So it makes sense to exercise your entire body during each workout to elicit a maximal hormonal/testosterone response.
http://www.fourhourworkweek.com/blog/2007/04/29/from-geek-to-freak-how-i-gained-34-lbs-of-muscle-in-4-weeks/Please note that I am not an expert, these are just my personal experiences. Hope this helps!