Will the power resistor not affect the current output?The output voltage may be rather higher unless the transformer is delivering its full load current. Since you have a 3A transformer, this may be the case even at full load using a 1A regulator.
You might find that adding something like a power resistor in series with the output from the reservoir capacitor helps to lower the regulator dissipation, but if you do that don't forget to add a fairly substantial capacitor between the regulator input and common.