We present a finite element analysis of a diffusion problem involving a coated cylinder enabling the rotation of heat fluxes. The coating consists of a heterogeneous anisotropic conductivity deduced from a geometric transformation in the time dependent heat equation. In contrast to thermal cloak and concentrator, specific heat and density are not affected by the transformation in the rotator. Therein, thermal flux diffuses from region of lower temperature to higher temperature, leading to an apparent negative conductivity analogous to what was observed in transformed thermostatics. When a conducting object lies inside the rotator, it appears as if rotated by certain angle to an external observer, what can be seen as a thermal illusion. A structured rotator is finally proposed inspired by earlier designs of thermostatic and microwave rotators.