In collaboration with groups from Spain and Italy we have written a paper on how temperature effects the radius of skyrmions. This is caused by the change in the effective magnetic parameters due to spin fluctuations. We can calculate the temperature dependence of the relevant magnetic parameters such as anisotropy, exchange stiffness and Dzyaloshinskii-Moriya interaction (DMI) using atomistic spin models.
Interestingly, my friend Unai Atxitia was also conducting a very thorough study of the temperature dependence of the DMI (https://arxiv.org/abs/1706.01684). Using different methods and working independently we found the same results for the DMI scaling which is a nice cross check with each other. I highly recommend reading his paper which includes some really interesting details such as an emergent anisotropy contribution from the DMI.