Burning doesn't seem like the right word. Its more of a pain during urination, but only after orgasm. No fevers.
This sounds like you have an infection of the prostate called prostatitis. This can occur from long periods of sitting or bike riding that puts pressure on the prostate. You need to get in to see your doctor or a urologist for a prostate exam and a urine culture and you'll need to be started on an antibiotic like ciprofloxacin for 30 days to treat this infection. You can take ibuprofen 800 mg every 8 hours for 7-10 days to decrease the inflammation of the prostate that is causing the pain. Hope this helps and let me know if you have questions. Just use reply. Thanks.