Summary: Originating micropolar microrotation vectors and pseudovectors of presumably integer weights is discussed. Overwhelming majority of publications on micropolar thermoelasticity deals with absolute tensors formulations, minority is devoted to applications of positive weight microrotation contravariant pseudovector to formulations of micropolar thermoelasticity. A negative weight microrotation pseudovector is not actually employed for derivation of hemitropic thermoelastic equations as it may be concluded from a literary search. The present paper is devoted to this issue. Thermodynamic state potentials for hemitropic thermoelastic continuum are proposed in terms of asymmetric strain tensor, wryness pseudotensor of negative weight and the entropy. In virtue of contravariant algebraic treatment of translations and microrotations general algebraically consistent coordinate representations for constitutive fourth rank tensors and pseudotensors are considered in terms of the metric tensor and the constitutive hemitropic pseudoinvariants, then replaced by the conventional constitutive pseudoscalars. Energy and entropy balance equations are obtained to provide thermodynamic consistency of the proposed model. Coupled hemitropic thermoelastic equations are represented in terms of contravariant displacement vector and negative weight covariant microratation pseudovector.