Ignoring R4 for the moment, its effect is negligible, I don't understand what its purpose is.

The circuit is not functioning as a comparator. The closed loop circuit will attempt to balance the inputs of the opamp. It will adjust the voltage at V2 until the self-heating of the thermistor causes the thermistor resistance to be about 39 ohms.

Redrawing the circuit makes it easier to understand.

^{simulate this circuit – Schematic created using CircuitLab}

Ignoring R4 for the moment, its effect is negligible, I don't understand what its purpose is. Edit: Necessary to boot the circuit (thanks Transistor).

The circuit is not functioning as a comparator. The closed loop circuit will attempt to balance the inputs of the opamp. It will adjust the voltage at V2 until the self-heating of the thermistor causes the thermistor resistance to be about 39 ohms.

Redrawing the circuit makes it easier to understand.

^{simulate this circuit – Schematic created using CircuitLab}

Edit: This circuit may work in a laboratory environment, but I question its usefulness in the real world. On a cold day, I doubt that you can ever get enough power into the thermistor to warm it up. The thermistor's resistance on a cold day might be 1k. 5V^2/1k is only 25 mW.