Effects of temperature T (6-18 K) 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 is 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)T2]-1 depends significantly on both τq and T where the first term κ∼τq-1/2 decreases with τq. The second term is proportional to the 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. The presented model accounts memory effects and yields η=3/2.