See if you can carefully put the thermometer back together. It uses "Zebra strips" to make the connections.
You need a display module - a display plus a driver PCB. Keep looking for small display modules on eBay/ Google but unless it is fully assembled with a driver with MCU interface, you are going to get nowhere with it.
Probably your best bet is a "0802" display or a Nokia 5110.
If you want a much smaller display, you will actually find that LEDs are more practical.