I understand what you mean, however, the temperatures you give seems extreme... if it really gets above 150 in my car... the interior would start melting ...
The LCD can operate well from -10Cdeg to 45CDeg (I took 5 of from max, because it will operate at 50, but screen showing blury, above 50 screen is white with black stripes, below 45 it seems to operate good).
Hope this helps, I could maybe even fix this on the diagram on board... and not make it adjustable...
Which should make the switch easier to make.
The fans run on ignition, thus it will always operate when the key is turned on which is fine, but the LCD should only be turned on when under 45Cdeg.