A dermal applicator device may include a housing having a retainer configured to hold and engage a spherical surface. A reservoir, containing a liquid, is contained within a shell that is at least partially spherical but at least has curved surfaces supporting rotation. The shell may be engaged within the retainer to permit relative rotation of the shell with respect to the housing. The liquid may be selected to have a freezing point below 0° C. and/or a specific latent heat of fusion higher than water. The shell may further include an outwardly protruding lug extending from its surface, and the housing may be configured to form an orbital chamber between an inner surface thereof and the shell when the shell is retained in the retainer. The protruding lug is constrained within the orbital chamber such that rotation of the shell relative to the housing is restricted.