Output from TD100 with instrumentation amplifier not as expected
It should (typically) work to have ~410mV out at room temperature. So I suspect an error in the wiring or an incorrect or damaged part.
Note carefully however that the OA1 is called upon to sink Vdiff/5K, so for 3V out it will have to sink about 62uA with an output voltage of about -160mV. Obviously, it won't do that with a single +5V supply.
In fact, it will run out of sink capability well before that, if you look at the datasheet- around 25uA (typically, at room temperature) with a 5V supply. The LM324 behaves well with a grounded load, but it has only a weak current sink to allow the output to approach Vee when it is called upon to sink current.