If the PC uses very little power, is it safe to completely turn off the PSU fan ?

My work PC has Athlon 200GE, no graphics card, one regular SSD, one M.2 SSD and two RAM sticks. Yesterday I guess a small spider crawled into my power supply and it became noisy. When I removed it I saw small web pieces on the grill. I replaced it with my spare power supply which is a overkill OCZ 700W 80 plus modular unit from way back in 2009 and has a big case fan that I installed in it, I don't remember why, I guess I thought the original fan was noisy. The problem is that this fan has molex connection and works at 100% and is a bit noisy itself. Is there any risk of overheating if I don't use the fan at all? I guess my PC uses well under 100W most of the time.