To downsize the thermometer further, I replaced the Arduino UNO with an ATtiny85. The Arduino sketch has to be modified in order to match the ATtiny pin layout.

#include <LiquidCrystal595.h>
float tempC = 0;
float tempf = 0;
int tempPin = 3; // AtTiny
float samples[8]; 
float maxi = 0, mini = 100; 
int i;

//Initialize the library with datapin, latchpin, clockpin, num_lines
//LiquidCrystal595 lcd(2,3,4); // Arduino
LiquidCrystal595 lcd( 0, 1, 2); // AtTiny

void setup()   {
   lcd.begin(16,2);
   lcd.setCursor(2,0);
   lcd.print("LM335Z");
   lcd.setCursor(3,1);
   lcd.print("Thermometer");
   delay(5000);
   lcd.clear();
   lcd.setCursor(2,0);
   lcd.print("reading ...");
   lcd.setCursor(1,1);
   lcd.print("...done!");   
delay(5000);
lcd.clear();
}
void loop() {
  for(i = 0;i<=7;i++) {
   samples[i] = (( 5.0 * analogRead(tempPin) * 100.0) / 1024.0) - 273.15;
  lcd.setCursor(0,0);   
  lcd.print("Current temp is: ");
  lcd.setCursor(1,1);  
  lcd.print("  Celsius   ");
  lcd.setCursor(12,1);  
  lcd.print(samples[i]);                                     
  tempC = tempC + samples[i];
  delay(800);
  }
 tempC = tempC/8.0;  
 tempf = (tempC * 9)/ 5 + 32;
 if(tempC > maxi) {
     maxi = tempC; }
 if(tempC < mini) {
    mini = tempC; }
 lcd.setCursor(0, 1);
 lcd.print(" Fahrenheit ");
 lcd.setCursor(12, 1);
 lcd.print(tempf);
 delay(5000);
tempC = 0;
}