We study the high temperature regime within the glass phase of an elastic object with short ranged disorder. In that regime we argue that the scaling functions of any observable are described by a continuum model with a $delta$-correlated disorder an
d that they are universal up to only two parameters that can be explicitly computed. This is shown numerically on the roughness of directed polymer models and by dimensional and functional renormalization group arguments. We discuss experimental consequences such as non-monotonous behaviour with temperature.
