An ideal Carnot engine is composed of two reservoirs and a working fluid. The hot reservoir and the cold reservoir have temperatures $T_1$ and $T_2$ respectively, with $T_1>T_2$. The working fluid is in a phase transition and has temperature $T_1$ at the start of the Carnot cycle. It undergoes another phase transition at $T_2$ at the end of the cycle to return to its original state.
This is a P-V diagram of the Carnot cycle which proceeds in four steps:
I'm particularly interested in the two stages (from 1 to 2) and (from 3 to 4). They can be described as follows:
1) Stage (from 1 to 2) is a reversible isothermal expansion of the working fluid to transform from the liquid state to the gaseous one. The working fluid is at $T_1$ and it happens to have boiling point at $T_1$. Hence, heat $Q_1$ is supplied to the fluid from the hot reservoir until it transforms to a gas keeping its temperature constant along the whole process. (That the fluid's temperature is constant during the whole process is owing to it being in a phase transition.)
2) Stage (from 3 to 4) is a reversible isothermal compression, and it's similar to what we have just described, with the difference being in this case, heat $Q_2$ is drawn out of the fluid and transfers to the cold reservoir, and the fluid transforms from gas to liquid retaining a constant temperature of $T_2$ throughout the whole process.
I'm puzzled by the mechanism by which the working fluid undergoes phase transition. So, at stage (from 1 to 2), both the fluid and the hot reservoir have the exact same temperature, so that they're in a thermal equilibrium. Hence, there should be no heat or energy exchange between the two bodies. The same can be said of stage (from 3 to 4).
So how is it possible for heat to flow from two bodies having the exact same temperature?