Over a small temperature range, driven by a more-or-less constant current, you can probably find a NTC thermistor of about the right tempco. The impedance will just be that of the resistance which may not be suitable, but the requirement of low voltage is a difficult constraint.
If you relax the latter, you could simply use a transistor as a shunt regulator with a resistive divider: R1 from collector to base, R2 from base to emitter, with the tempco of the B-E diode multiplied by (1+ (R1/R2)). But Vbe is also multiplied by the same amount, so for 12.6mV/C you will have a collector-emitter voltage of about 3.7V (some call this circuit a Vbe multiplier). There is another term working against the negative tempco of Vbe, due to the beta going up with temperature; thus, the lower base current loading of the voltage divider with increased temperature causes the base-emitter voltage magnitude to rise a bit due to that.
If you must have a 1V level with that tempco, provided you have other higher voltages in the circuit available you can offset the ~3.7V with a stable ~2.6V and get the desired one volt.
