I built a pump control circuit using a 741 as a comparator, driving a TIP120 (Darlington transistor) to run the pump. (Those are the parts I've got)
I used a NTC thermistor to sense the water temp. (not waterproofed and tested in water yet, air only) I got some interesting quirks, and I think I got the bugs worked out, but I have some questions.

If the inverting input is floating, will the voltage follow the non-inverting input? (I think my pot was not connected fully)

After I got the first issue resolved, the pump would not fully shut off. Is this because the output of a 741 with a single supply never really goes to zero? It worked much better when I connected a 2.2k pulldown resistor to the base.

I'm hoping I got it right this time and didn't miss something. (Multisim didn't have a TIP120)

Thanks in advance.

 

I built a pump control circuit using a 741 as a comparator, driving a TIP120 (Darlington transistor) to run the pump. (Those are the parts I've got)

Without belaboring the point too much, a 741 is an ancient opamp that was the greatest thing since sliced bread when it first came out, but it was quickly surpassed in performance by many other opamps. Educational institutions still use them, because they perform so poorly that not even starving students would steal them.

They're really supposed to have ±15v supply rails, and according to the specs, they have a hard time getting within about 4v of either rail (they might actually get within 2v), which is why you had a hard time getting the TIP120 to turn off.

You should have at least a 1k resistor between the opamp output and the TIP120 base.

I used a NTC thermistor to sense the water temp. (not waterproofed and tested in water yet, air only) I got some interesting quirks, and I think I got the bugs worked out, but I have some questions.

If the inverting input is floating, will the voltage follow the non-inverting input? (I think my pot was not connected fully)

It'll be unpredictable.

After I got the first issue resolved, the pump would not fully shut off. Is this because the output of a 741 with a single supply never really goes to zero?

Yes, it never really gets anywhere close to zero.

It worked much better when I connected a 2.2k pulldown resistor to the base.

Like I mentioned above, you still need a 1k or higher resistor between the 741 output and the TIP120 base.

 

With the (-) input floating (no voltage) and any positive voltage on the (+) input of the comparator, the 741 will make its output voltage as high as it can. It will not follow, it will sort of quickly jump there. 741's are not fast at all.

A BCX38 is a darlington transistor, its base must exceed 2 Vbe's to turn on (~1.4v), and conversely the base must be below that to turn off. Your circuit ran better with the 2.2k resistor because it loaded the 741's output which caused its "low" voltage to squat a bit lower than it was without that resistor thus allowing the '38 to turn off. That is not the ideal approach to shut off a transistor.

You will need hysteresis to calm the circuit as the thermistor slowly crosses the comparator's switching point otherwise there will be considerable dithering at that point.

 

The 1k resistor cleaned up the switch quite a bit! I know i'm using a whiffle bat in a fast pitch game, but radio shack is the only walk in source I've got, and any time I order from places like Jameco or E express, I always need stuff I didn't think to order, and shipping costs add up. Thanks again!