Hello again,
Here are the two equations that describe your current circuit values:
R4=((Vs1-Vs2+Vb-Va)*R5)/(Va-Vb)
Vo=((-Vs1+Va)*R5+Va*R4)/R4
where
Va is the voltage that will appear out of the LM35 with your first set point (upper, 8 degrees),
Vb is the voltage that will appear out of the LM35 with your second set point (lower, 5 degrees),
Vs1 is the upper source voltage,
Vs2 is the lower source voltage,
Vo is the output setting of the top op amp,
R5 is of course R5 in your schematic,
R4 is R4 in your schematic.
Since your upper set point is at 8 deg and the LM35 response is 8*0.010, the upper set point voltage Va is equal to 0.080 volts.
Similarly, the lower set point is 5*0.010 so the lower set point voltage Vb is 0.050 volts.
Vs1 is the source supply voltage after the drops from the transistor and diode and LED, so we'll start with an estimate of 8 volts.
Vs2 is the negative supply voltage which due to two diodes in series is about 1.4v, but it's negative so Vs2 is equal to -1.4 volts.
R5 is of course 10k but we'll work in units of k ohms so R5 is equal to 10.
Plugging all these into the two equations we get:
R4=((Vs1-Vs2+Vb-Va)*R5)/(Va-Vb)
R4=((8 - (-1.4)+0.050-0.080)*10)/(0.080-0.050)
and doing the math we get:
R4=3123.33333333333
which is in k ohms, so R4 is approx equal to 3123k.
The op amp output set point is:
Vo=((-Vs1+Va)*R5+Va*R4)/R4
Vo=((-8+0.080)*10+0.080*3123.3333)/3123.3333
so doing the math we get:
Vo=0.05464 approximately.
This means R4 will have to be 3123k ohms and the output of the op amp will have to be adjusted to approx 55mv.
This was using the approximations of 8v and -1.4v for the two source voltages, so if they are not that (you can measure them first and do the calculations over again if you like) you will have to redo the calculations and find the new value of R4.
Also, if noise is still a problem (and it most likely will be) you will have to try the other suggestions of adding the caps and resistors (previous post).
If it doesnt work after that it could simply mean that something is not connected properly.