Polymers in disordered media are examples of random Gibbs measures on directed paths moving through a random environment. Such disordered systems often exhibit complex landscape behavior rich with multiple valleys which act as metastable states. This generic property manifests in multiple forms, in particular in the fragility or extreme sensitivity to perturbations. Namely, a slight variation in external parameters such as the disorder or the temperature causes a profound change in the system, often termed as chaos. In experiments, typically temperature plays the role of a prototypical control parameter since it is easier to vary than the disorder. However, on the mathematical side, studying disorder chaos is easier since it involves infusing the system with extra independent randomness. In this talk, we will report some progress, based on forthcoming work with Victor Ginsburg and Zoe Himwich, in understanding temperature chaos in the Kardar–Parisi–Zhang universality class with the Continuum Directed Random Polymer being the model of investigation. Time permitting, a connection between temperature and disorder chaos will also be explored.