According to the data you provided (darker iris), you might be experiencing pigment dispersion syndrome (PDS). Pigment dispersion syndrome is a condition in which the pigment from the iris is released in the posterior eye chamber due to increased contact between posterior iris and zonular fibers. The pigment follows the flow of the aqueous in the anterior chamber, where it might block the aqueous drainage and cause glaucoma. The glaucoma is actually the real problem that has to be treated if one develops. The sole pigment dispersion syndrome is asymptomatic and only controls for glaucoma are needed to prevent damage to the retina caused by the glaucoma.
You might want to visit an ophthalmologist to check if the darker iris is caused by pigment dispersion syndrome. Examination of the anterior chamber of the eye would be needed. The intraocular pressure would be measured to check for glaucoma. If glaucoma is found, then the doctor might recommend eye drops in mild cases or eye surgery in more severe cases of glaucoma.
No data can be found that might indicate that heat can affect iris pigmentation.