I would expect a different temperature distribution. A thermal chamber will heat up uniformly. The nominal current might create temperature gradients. And those will for sure influence thermal EMF. For most of the cases it will give you a reasonable value.
One trick I use to evaluate thermal EMF in function of the current is to use AC test currents to heat up the shunt and a DC voltmeter to measure EMF (the voltmeter will filter all the AC component and measure only the offset). That's good when you don't have a DC high current supply since you can use any cheap transformer rewound for high currents (I used a free microwave oven transformer, good up to 400A).
Then I measure the resistance at lower DC currents and temperatures.
The photo shows some tests of a DIY low value resistor (I made it to measure pulsed currents, thats why I'm using a BNC). In the first plot there are temperature and EMF in function of AC current. In the second plot there's DC resistance (at just one temperature).
Next step would be to use both DC and AC current to heat up the shunt and measure its resistance at the same time, but I didn't had time for that, jet.