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We study the local regularity of $p$-caloric functions or more generally of$\phi$-caloric functions. In particular, we study local solutions of non-linearparabolic systems with homogeneous right hand side, where the leading terms hasUhlenbeck structure of Orlicz type. This paper closes the gap of [22] whereLiebermann proved that if the gradient of a solution is bounded, it is H\"oldercontinuous.  The crucial step is a novel local estimates for the gradient of thesolutions, which generalize and improve the pioneering estimates of DiBenedettoand Friedman [12,10] for the $p$-Laplace heat equation.

Regularity for parabolic systems of Uhlenbeck type with Orlicz growth