I guess that you are using the "clockwise pin mapping" compiler option for the ATTINY84 otherwise you have a conflict between digital pin 3 (used by the LCD) and analog pin 7 (used by the sensor).
To troubleshoot further, I'd suggest first of all writing the raw value of analogRead(Thermostat) to the display (maybe once per second) simply to see the state of the source data. If that is highly random, then no amount of smoothing will help. If it is, however, consistent, then you have to suspect your processing.
You could also look at a moving average type smoothing rather than a simple average over blocks of 5 results.