fan is working slowly. my computer is heating up.

Depending on how long you have had the laptop it may just need a cleaning . over time the fan fills up with dust and forces dust into the heat sink making cooling a difficult thing . You can try blowing compressed air through the vents of the laptop . Blow air both ways through through the vents . some people have had sucksess(Pun intended)with a vacuum if you do choose to use a vacuum don't use the metal end of the hose make sure you only press a plastic part to the laptop. A vacuum can create static electricity and short the laptop if you use the metal end of the vacuum so make sure you use plastic against the laptop.If you have no joy and you laptop continues to overheat you may want to do a more thorough cleaning by taking the laptop apart and getting right into the fan and heat sink. This guild can help get into the laptop

Toshiba Satellite P55W Hard Drive Replacement

If all else fails and you do want to replace the fan don't forget to replace the thermal paste when you seat the fan. If you have never done this there are lots of videos on you tube to show how its done. Hope this helps