The transport process of a Brownian particle in a ratchet-like potential su
bjected to two exchanging Gaussian white noises is studied. The change of t
he temperatures is described by a stochastic dichotomic process. By making
use of the perturbation method the probability current up to second order i
n small correlation time tau is obtained, and time-averaged current is eval
uated numerically for a whole region of the parameters. For asymptotically
fast temperature cycles, the present model yields larger current in compari
son with the periodical temperature cycles. Depending on the temperature of
cold heat reservoir, the current changes sign as a function of tau.