Doug Natelson, writes one of the few blogs on condensed matter physics. He recently wrote a blog on What is temperature? I don't really like his perspective. I think it is best to define temperature in macroscopic and operational terms, using the zeroth law of thermodynamics. The attached slides are from my undergraduate lectures. The key ideas are
* the zeroth law allows us to assign a single number to a thermodynamic system that has the important property that this number will tell us whether or not the system will change when it is brought into thermal contact with another system.
* a thermometer is just a thermodynamic system with just one state variable.