The dynamics of a qubit in two different environments are investigated theoretically. The first environment is a two level system coupled to a bosonic bath. And the second one is a damped harmonic oscillator. Based on a unitary transformation, we find that the decoherence of the qubit can be reduced with increasing temperature T in the first case, which agree with the results in Ref. [8], whereas, it cannot be reduced with T in the second case. In both cases, the qubit dynamics are changed substantially as the coupling increases or finite detuning appears. (C) 2010 Elsevier B.V. All rights reserved.