Can an overactive thyroid cause burning feet and weird circulation to the extremities?

I think so: Hyperthyroid hormone levels increase the metabolic activities of almost all tissues of the body. The basal metabolic rate can increase to as much as 60 to 100% above normal. This will excite areas of activity including effecting blood flow to the skin and other areas as well as increasing the likelihood of extreme nervousness with multiple psychoneurotic tendencies such as anxiety complexes etc.

See below: Burning feet yes but not sure what you mean by weird circulation.

It's possible...: The thyroid is a major regulator of several systems within the body. It is possible that it can influence nerves and in turn, circulation. Talk to your endocrinologist about your symptoms.

Possible: Symptoms of overactive thyroid include weight loss, heat intolerance or feeling unusually hot though not just in your feet, tremor or shakiness if hands and feet, racing heart beat, anxiety,tiredness, prominent or bulging eyes. Overactive thyroid speeds up your metabolism but not necessarily your circulation. You really cannot feel your circulation, so you may be describing another symptom.