Thanks for your query. Burning sensation in the thigh when you were lying down points towards a possibility of irritated nerves supplying that area. Sometimes sitting or lying down in a particular posture causes irritation of the nerves or spinal nerves which can cause burning sensation or numbness/ tingling
in that area.
The other possibility from your history of high cholesterol
is of peripheral vascular disease
. High cholesterol is responsible for causing plaques in the blood vessels which may impair blood flow especially to the extremities causing a burning sensation in that area. Although at your age, this possibility is less likely, but cannot be ignored since there is history of high cholesterol.
Third possibility is of vitamin B 12 deficiency or diabetes
. Vitamin B 12 deficiency can occur in people especially if you are a vegetarian. Take some vitamin B 12 supplements for some days and get your blood sugar levels checked if the repeat happens.
Hope this answers your query. If you have additional questions then please do post us. Wishing you good health.