Effects of temperature T (6K-18K) and variable in-situ static disorder on dissipative resistance of two dimensional electrons are investigated in GaAs quantum wells placed in a perpendicular magnetic field, B ⊥. Quantum contributions to the magnetoresistance, leading to Quantum Positive MagnetoResistance (QPMR), are separated by application of an in-plane magnetic field. QPMR decreases considerably with both the temperature and the static disorder and is in good quantitative agreement with theory. The remaining resistance R decreases with the magnetic field exhibiting an anomalous polynomial dependence on B ⊥ : R(B ⊥) − R(0)) = A(T, τq)B η ⊥ , where the power η ≈1.5±0.1 in a broad range of temperatures and disorder. The disorder is characterized by electron quantum lifetime τq. The scaling factor A(T, τq) ∼ [κ(τq)+β(τq)T 2 ] −1 depends significantly on both τq and T , where the first term κ ∼ τ −1/2 q decreases with τq. The second term is proportional to square of the temperature and diverges with increasing static disorder. Above a critical disorder the anomalous magnetoresistance is absent and only a positive magnetoresistance, exhibiting no distinct polynomial behavior with the magnetic field, is observed. Presented model accounts memory effects and yields η =3/2.