Alternative Wheatstone bridge for thermistor - Interpretation needed
I understand the 2nd circuit but not the 1st one. Explain how the 1st circuit can even work because I do not see how it can even work. It simply makes no sense to me.

The 2nd circuit a reference voltage using R2 and R3 and (the opamp) compares that to a varying (over temperature) voltage made by R1 and the thermistor.

When the resistance of the thermistor rises due to low temperature, the voltage at the + input of the opamp rises. When it becomes larger than the reference voltage at the - input of the opamp, the output of the opamp becomes "high" (switched to positive supply rail) which will switch on Q1 and therefore the heating element.