Try using diagnostics to determine if the fan is the problem or if some other component is failing. To get into Diagnostics, hit F10 when you see the Dell Logo and choose Diagnostics. Diagnostics usually will do a check of all components or you can choose a particular component to test, start with the basic check for all components and if all the diagnostic routine pass then try the comprehensive mode.
Dell warranty is usually a year but there is an extension, you can go to the Dell website to confirm your warranty. If it is still in warranty then call Dell Tech support and they will diagnose it and dispatch a tech with a part within a few days (usually next day)