This is a new thermostat right? Try removing the thermostat altogether (this is OK, the early A4's didn't even have one) and see if this improves the water flow.
If you are getting good flow to the thermostat, then the pump is probably fine. Check the other connections - the crossover tube between the head and the manifold and the water outlet on the manifold are common trouble spots.
If this is a raw water cooled A4, then there is a good possibility it has built up enough scale and sedimentary deposits to cause a blockage. The best way to fix this is with an acid flush. Run a 1:3 water and muriatic acid solution through the engine and then flush well with fresh water. If you can identify the blockage, you can soak the offending part in a stronger solution.
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