I would add a couple of suggestions for the design:
You are using 741 OP-AMP, which is not rail-to-rail, and you're using it for driving the base of a transistor: what happens is that when the output of the 741 is high, it will be at about Vcc - 1V, that is enough to keep the transistor on. I would suggest using a rail-to-rail OPAMP or adding a small resistance to the emitter of the transistor to limit the current when the input is high (could be even better because you mantain the fan at a slower speed but still cooling).
When designing with sensors, such as photoresistors or thermistors, it's better to - first know the value at room temperature of these sensors - and then picking a potentiometer just bigger to simulate the behavior of this sensor, and check that the circuit is working.
UPDATE: from the datasheet, the typical voltage swing is 13-14 V (you can measure the exact maximum value just measuring the positive saturation voltage), and by design the lose in the range tends to be more in the upper rail, because the output stage has a \$ {V_{CE}}^{sat} + {V_{BE}^{ON}} \simeq 0.2 + 0.6 \simeq 0.8 V \$.
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UPDATE 2: Now I see that you are powering your circuit at +12V / 0V, that is NOT the exact supply voltage specified for the 741 OPAMP: it requires a dual-rail, \$ \pm 15V \$ fix this as the first thing.
You can see as your OPAMP is outputting 10 V instead of 12, and 1.2V instead of 0; the first, with the drop over the resistor, makes the transistor always on, as you can see that the base voltage is 11V, enough to keeping it on.
And...why did you use a diode to simulate a fan??? Seems a quite different load.
UPDATE TO THE UPDATE:
I'm glad that it works, at least the simulation: however, you are still using a single rail supply (+12:0, +15:0). The 741 wants +15:-15, so the best thing to do is CHANGING THE OPAMP. It's not expensive at all and you can use a rail-to-rail (again), that is better for single supply applications, down to 3.3V if you need that; or, for your case, +12 or +5.
This is an option, here there is plenty, you have only to choose, based primarily on availability for your purpose. For the simulator, you can also find many options.
1-2 degrees is an easy resolution (even when you mean accuracy, which is not the same!). I would consider LM75 and it various clones, or a DS1820/18S20/18B20/1822. Microchip has a lot of temperature sensors, including LM75 clones for < $1. The voltage output versions are cheap, but I would prefer a digital one.
Best Answer
As you usually need just few mA, the only concern is temperature stability of your opamp & passive components around it. Bridge circuit & precision refV source of ADC usually handle that, but in your case it's much much harder.