Loud fan and temperature gauge going up slowly?

So, my radiator fan sounds loud after 15 minutes of driving. The temperature gauge stays at the halfway mark when I’m driving. But when I’m idle the gauge very slowly starts to go up. I would say in a span of 3-5 minutes it nearly reaches the red line. But once I start driving it goes back to the middle mark. Should I replace the radiator fan? The radiator hoses are hot to the touch, so I don’t think anything is leaking.