You could try the following circuit:



If you make Vref/2 = 1.5V, then you can use LM324 powered by +5V, as then their output voltage range is capable to deliver 3V.
When temperature varies between -20°C and +70°C, then LM35 outputs -0.2V to +0.7V. The first amplifier stage multiplies this differential voltage by a factor of '3'. Second amplifier stage removes the common mode voltage caused by the two diodes at LM35 and shifts the result by 0.75V, means adds an offset of 0.75V, so that signal cannot become negative!
So, at temperature of -20°C a voltage of 3 x -0.2V + 0.75V = 0.15V is provided at output (VIN+). At 0°C a voltage of 0.75V can be seen and at +70°C the output voltage is 3 x +0.7V + 0.75V = 2.85V.

Adjust the trimmers at two well known temperatures, where one should be 0°C (ice water)! At this temperature the trimmer at LM336 is adjusted so that exactly 0.75V can be seen at 'VIN+'. The other trimmer adjusts the other temperature.
These both trimmers are needed, because the resistors and offset voltages of involved OPamps will add some errors, although LM35 alone might be precise enough.

Good luck,
Kai