  Providing the microscopic behavior of a thermalization process has always
been an intriguing issue. There are several models of thermalization, which
often requires interaction of the system under consideration with the
microscopic constituents of the macroscopic heat bath. With an aim to simulate
such a thermalization process, here we look at the thermalization of a
two-level quantum system under the action of a Markovian master equation
corresponding to memory-less action of a heat bath, kept at a certain
temperature, using a single-qubit ancilla. A two-qubit interaction Hamiltonian
($H_{th}$, say) is then designed -- with a single-qubit thermal state as the
initial state of the ancilla -- which gives rise to thermalization of the
system qubit in the infinite time limit. Further, we study the general form of
Hamiltonian, of which ours is a special case, and look for the conditions for
thermalization to occur. We also derive a Lindblad-like non-Markovian master
equation for the system dynamics under the general form of system-ancilla
Hamiltonian.
