[syhprum (OP)]

In experiments with Bose condensates we read of temperatures of a billionth of a °K being achieved, can temperature be varied to an infinitesimal degree or is there a quanta of temperature.

[Mr. Scientist]

Yes. Temperature is related to quanta - always will be too so long as thermodynamical systems are invariant within the spacetime fabric. Quanta is termodynamical, so you could say the vacuum is a thermodynamical sheet of quantum fluctuations

[yor_on]

In black body radiation the steps are discrete, jumping sort of in a non smooth manner. and as radiation is just another form of describing temperature it seems reasonable to expect temperature to contain the same mechanism. Then again, intuitively I would prefer temperature to be a smooth process but I don't think it is.