If it's the CPU fan... I wouldn't run it at all. CPU's can burn up in minutes or sometimes even seconds. Doesn't take them very long at all to get hot.
It sounds like it's a case fan that went out, which isn't that big of deal in the short term, you do want to get it replaced though so you can have proper air circulation inside the case. You can take the cover off your case and sit the computer out in the open until you can get it replaced... the ac in the house can help somewhat but then you gotta worry about dust.... but that's never been a problem with me when I've done it.