In the default state, the temperature is displayed on the display.
When button 1 is pressed: the system records ten temperatures at one-second intervals, with some form of indication to show that it is gathering data. When data collection ends, the system should return to the default state, and give some form of indication that it has done so. The temperatures recorded should be stored for later use.
When button 2 is pressed, either:
If there are stored temperatures in memory, the system displays them.
If there are no stored temperatures in memory, the system indicates this.
Can someone give me some advice about the code, please?
Read the state of a button?
Use an if-statement to do something based on the state of a button?
Turn on an LED?
Read a temperature sensor?
Convert the temperature input to a Centigrade or Fahrenheit?
How to address LEDs with a shift register?
If you don't know how to do any of this stuff, look-up some examples and take it one step at a time...
That LED requires a "push-pull" connection (something like a matrix). You drive one (or more) of the individual inputs high, then you pull-down one of the common pins to turn on the LED associated with the individual pin for the LED(s) you want to light in that segment. In order to address an LED in the other segment, you need to pull that segment's common pin low. That means you can only address one segment at a time, so you'll have to switch back-and-forth faster than the eye can see.
You may have enough I/O pins that you don't need a shift register.