If you wait until thermal equilibrium is reached in the water, no.
But, you said:
We can assume 30 seconds pass after removing from the heat sources before testing.
In which case, if you put enough temperature sensors into the water to create a 2D or 3D profile of the water, perhaps, or maybe even probably, because maybe there will be a temperature gradient throughout the water that differs for microwave heating vs flame heating. The flame being applied to the bottom would result in the hottest water on the bottom, whereas the microwave might be more evenly heated, or perhaps have hot spots interspersed in the water. This would be interesting to test.
See also this comment. A thermal camera might be used too.
And with the update:
They both get poured into identical new containers before testing.
Back to "no" again, once you've disturbed the original heat gradient, unless a unique heat distribution "signature" resulted from each type of heating.
Note that this signature might be in the form of a thermal camera video of the water after being poured, rather than in the form of a picture, because the pouring process would be very dynamic.
This would be a fun thesis to work on. AI and machine learning might be trained on thermal video samples of this pouring being done for both heating types and then be tested to see if it can accurately determine the way the water was heated by looking at the thermal video of the water during or just after being poured. Even if humans can't pick up clear thermal patterns, maybe AI and computers can.