The interior must be clean and free from dust.
The same is said for the interior of the PSU and the interior of the heat sink assemblies.
Fans that ramp up, then down may be due to a sensor malfunction, or may be due to power management issues.
Reset of the SMU may be in order:
Failing that, find a copy of the ASD 2.5.8, burn a CD, boot to the disc and run Thermal Calibration.
Keep the Radeon clean, and consider replacing thermal compound: