I would not use a thermometer with a shunt unless it was designed to accept one.
Does your shunt bolt to a heat sink? If you get a TO-220 shunt, bolt it to a heat sink that has a temperature sensor attached this might be enough to get a bit more accuracy.
Also, maybe you can just get the heat sink big enough so that the shunt drift is reduced @ max temperature.. or just put a simple temperature activated fan on the heat sink.
regardless of what you do a heat sink will help you. I bet you would actually get pretty good performance if you put a TO style temperature sensor against the heat sink....
OR use a over sized regulator with a thermal pad on it, and attach a sensor to the thermal pad (imagine back to back to-220). You can assured there will be a low thermal resistance between the sensor and the resistor at this point.. so long you can handle the dissipation without the heat sink (it might cause your resistor to actually drift if its really hot all the time)...
Or you can take a heat sink which accept your shunt, drill a small hole through it, enough for the temperature sensor to slide through and contact the thermal transfer pad on the back of the shunt, so you can have direct thermometer contact and a heat sink (to possibly reduce shunt drift due to temperature). Then use some thermally conductive glue to seal it in there, should be decent.