Thyroid... Because this pituitary area is next to an area which produces thyroid-stimulating hormone, the prolactinoma may be causing or related to decreased thyroid function (hypothyroidism) which can result in heat intolerance.
Usually not. Unless the excess prolactin decreases lh and fsh causing hot flashes or the tumor is making TSH stimulating the thyroid to make excessive thyroid. Both are rare!
Not common. Common symptoms of prolactinoma are: headache, visual problem, abnormal milk production/flow, sexual dysfunction, infertility, breast tenderness...Heat intolerance is not a common symptom of prolactinoma unless this is how you feel when your estrogen level is low which can happen with a prolactinoma.