A lot actually depends on where you take it, what their service policy is and ultimately how much you pay

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Most services consist of opening the amplifier up, and first job:- cleaning out all of the dust from the heatsink and fan - if the amplifier is old then I often replace the fan since cooling is one of the most important area's of the Amplifier.
Often the engineer will check that there is no noise coming from the front pots (Level controls) and the Input / Output connections are all securely fitted to the printed circuit board, and that there is no noise or bad connections from these. Jack plugs are notoriously likely to wear and fail on older amplifiers where as modern Speakon style are more robust and easily likely to last the life of the amp.
Next it will be hooked up to a 4 ohm dummy load (Consisting of power resistors simulating a loudspeaker but without the noise) a signal will be fed into it, and the amplifier run at full power for a period, to check the correct operation of variable speed cooling fans, and to ensure that the amplifier is not overheating. If there are any signs of this then I often remove the heatsink, and add more heatsink compound to the surfaces and transistors where they meet the heatsink.
A scope (Oscilloscope) will be placed on the output to ensure that the the signal is smooth. The scope will also be used to check the DC which feeds the Amplifier to ensure that non of the smoothing capacitors (Which remove hum and clean up the supply) are passing excessive amounts of noise or indicating signs of failure.
Occasionally the protection circuitry may be tested, depending on the type.
It's important to make sure you get the details in writing of the service - many engineers will just clean the fans and hoover out the dust and charge you £25!. Just Like Mechanics there are good and bad engineers!!!

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The most important area of the service you can do yourself - such as cleaning the fans and removing dirt - Amps thrive on cooling, and (expensive) problems in the future usually result from failure to simply replace an £8 fan!.