The range of temperatures when the relay should be closed (i.e., when motor should be on) is 43° Celsius to 74° Celsius; that corresponds to an LM335 range of 3.15V to 3.45V.
I have several doubts.
1. The LM335 datasheet says, "Operates from 450uA to 5mA." Is the 8.2K resistor correct?
8.2K will give about 1mA which should be fine.
2. As configured, will the LM335 feed both halves of the IC1?
Yes.
3. What values of R1, R2, R3 give Vref1 = 3.15V and Vref2 = 3.45V? Could you show me how you calculated them? Should the R2 be a trimpot?
If the required accuracy of your setpoints is better than 5% then you need a trimpot. If so, then you should break the divider into two separate dividers (2 resistors and 2 trimpots) so you can adjust each setpoint separately without interaction.
Also the accuracy of your setpoints depends upon the accuracy of the 12V supply. For good accuracy you would should add a reference voltage to supply the resistor dividers.
4. The T77 comes in 3A and 10A varieties, same price. Is there any downside to using the 10-amp version for a 0.5-amp motor?
No downside unless the 10-amp verison requires more coil current.
And then, what feels like a difficult question.
5. The relay is good for 200,000 operations, so I'd like to add hysteresis. How do I add hysteresis to a window comparator?
You would add resistors in series with the positive input and then resistors from the output to each positive input.