The thermo emf of a thermocouple varies with the temperature $\theta$ of the hot junction as $E=a\theta +b{\theta }^2$ in volts where the ratio $a/b$ is $700^{\circ }\text{C}$. If the cold junction is kept at $0^{\circ }\text{C}$, then the neutral temperature is:

The neutral temperature ${\theta }_n$ is the temperature at which the thermo emf is maximum. This occurs when $\frac{dE}{d\theta }=0$.
$$E=a\theta +b{\theta }^2$$
$$\frac{dE}{d\theta }=a+2b\theta =0$$
$${\theta }_n=-\frac{a}{2b}=-\frac{1}{2}\left(\frac{a}{b}\right)$$
Given $\frac{a}{b}=700^{\circ }\text{C}$:
$${\theta }_n=-\frac{700}{2}=-350^{\circ }\text{C}$$
Since the hot junction temperature must be higher than the cold junction temperature ($0^{\circ }\text{C}$), a negative neutral temperature is physically impossible for this setup. Thus, no neutral temperature is possible.