LCD/display for a digital thermometer-like device
The smallest standard product LCD glass I could find is one from Varitronix that is 20.3mm x 38mm. It offers eight digits instead of 6. According to the data sheet for this part it is available with pins attached which adds a very small amount of additional width.

Note that for smaller sizes it is generally required to work with a vendor such as this to get a custom LCD glass made to your size requirements. Smallest size will generally imply that you use zebra strip for connections and a custom tooled case / holder to bring the display into proper contact and orientation with the circuit board. Do note that for small form factor displays it is common that the digit height is approximately one third the overall width of the LCD glass with the rest being used up by the contacts and sealing area.  




Varitronix Product Page
Above Product Data Sheet