Read temperature (DS18B20) with the ATTiny85
I would suggest it has to be the clock speed or memory. Whilst you can program the ATTiny85 with the Arduino IDE, it will take up quite a lot of its flash memory. There is a thread on the Arduino form here which might help pinpointing the issue.

One solution is to write it in AVR-C but I don't know if there is an easy way (or a library) for the 1-wire. I think you'll have to do it with the 1-Wire library alone as the DallasTemperature library is too much for the 8Kb of memory you have to play with.

Please feedback any breakthroughs you make as this is a nice project, the ATTiny is an awesome little chip...