What are the units pm/K? I can only think of picometres, but it doesn't seem to make sense. Here is the context, from the paper 'Towards Reproducible Ring Resonator Based Temperature Sensors', Klimov et al., Sensors & Transducers 191, 63 (2015):

Our results suggest that consistently high performance temperature
  sensors are obtained from the zone of stability (waveguide width > 600
  nm, air gap ≈ 130 nm and ring radius >10 µm) such that quality factors
  are consistent ≈ 104 and the temperature sensitivity is in the 70 pm/K
  to 80 pm/K range.

 A: From the paper, which states

fiber Bragg gratings (FBG) have been demonstrated to exhibit temperature dependent shifts in resonant wavelength of 10 pm/K

it is fairly clear that the unit is picometer per kelvin. That is, you have some device with a resonance wavelength $\lambda_\mathrm{R}$ which depends on temperature,
$$\lambda_\mathrm{R}=\lambda_\mathrm{R}(T)=\lambda_\mathrm{R,0}+\alpha (T-T_0),$$
where I've expanded linearly around $\lambda_\mathrm{R,0}= \lambda_\mathrm{R} (T_0)$. The sensitivity then has dimensions of length over temperature (consistent with $\mathrm{pm/K}$), and the range seems about right - a few parts per thousand increase in wavelength in the visible range for a $1\:\mathrm{K}$ temperature increase.
The temperature resolution of such a device is obviously going to depend, then, on the wavelength resolution of the spectrometer you're using to measure the resonance wavelength, so it cannot be inferred from the temperature sensitivity of the FBG/whatever it is you're using.
