When oven heats up the fan gets really loud and doesn't turn off for a long time

If your oven is fairly old, dust might be the enemy. FIRTS Turn off the breaker on your house electrical panel that feeds power to the oven before doing anything. Do not electrocute yourself!!

Remove the control console bezel where the control panel for your oven is..it's probably held on by a few screws. You'll see the fan is there somewhere inside the enclosre, it's purpose is to keep the circuit board cool but the fan grill is probably clogged with dust...remove the fan from the enclosure...try using a vacuum to get the dust out...you might need to use a small brush to loosen the dust film, clean the fan blades while you're at it. Reassemble and turn on the power ...you'll probably find the fan runs much quiter...good luck

You have to replace the fan , running for a long time after is normal its just cooling the oven