Fan Running On Full Speed

Hi! I recently acquired a mid 2010 white Macbook A1342. I knew the fan ran at full speed when the MacBook booted up, but was hopeful that NVRAM/SMC/PRAM resets might work, or the faulty battery might have been to blame. Unfortunately this doesn’t seem to be the case and, after running diagnostics I get an error code that seems to indicate a temperature sensor error. Is there any way of getting around this, or does the sensor need to be replaced? I can get the fan to operate normally using Macfans, but unfortunately the CPU seems to be throttled and the laptop operate so slowly despite an SSD and 4Gb of RAM. Any help and advice would be appreciated, even if it is to confirm the worst! Thanks.