Serial communication with the ATTiny85
When you say "nothing happens" ... something's happening, just you don't know what it is. Hook your circuit up to a logic analyser or run it through an AVR simulator so you can find out what is happening.

Also regarding serial comms, you could look at (https://github.com/nickandrew/avr-fd-serial) which is a software serial interface I wrote specifically for the ATTiny85; it's timer-driven so your tiny can do other things while communicating bidirectionally at 9600 bits/second.

I also wrote (https://github.com/nickandrew/avr-onewire) which implements the 1-Wire protocol for the DS18B20 sensor ... put the two together and that's a lot of the code for your project.