We study numerical solutions for parabolic equations with highly varying (multiscale) coefficients. Such equations typically appear when modelling heat diffusion in heterogeneous media like composite materials. For these problems classical polynomial based finite element methods fail to approximate the solution well unless the mesh width resolves the variations in the data. This leads to issues with computational cost and available memory, which calls for new approaches and methods. In this talk I will present a multiscale method based on localized orthogonal decomposition, first introduced by M\r{a}lqvist and Peterseim (2014). The focus will be on how to generalize this method to time dependent problems of parabolic type.