Neither Cold nor Hot Reservoirs are needed to run a Carnot Cycle.
The 'Carnot-Clapeyron-Kelvin' Work ratio actually does not remotely apply to the Carnot Cycle.
Why? Because heat in a Carnot cycle cannot be measured by temperature difference.

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Two last points.

No reservoirs needed

The Carnot cycle is often used to demonstrate why one needs both a cold and hot reservoir This is simply not the case.

One needs a heat source, chemical, friction, light could all replace a hot reservoir (and chemical usually does).

One does not need a cold reservoir, even for the Carnot Cycle. What is needed is a method of cooling, or allowing cooling to happen.

Consider a Carnot Cycle demonstration cylinder, placed in a vacuum, with a weight to hold pressure.

A light source, such as sunlight can replace the "hot reservoir".

Similarly, radiation can replace a cold reservoir during compression. Cooling would be slow, but steady. An isothermal compression could be done without contact with any physical body.

In general, a cold reservoir serves no purpose for most heat engines. They would behave the same whatever the outside temperature.

 

Temperature. difference does not equal quantity of heat.

In a Work Transfer Curve, temperature difference equates to a heat difference, with a constant multiple thrown in. Its easy to misconstrue this as measuring a quantity of heat in all engine cycles.

The Carnot cycle in particular CONSTANTLY adds heat during the isothermal expansion. The amount of heat is determined by the amount of expansion. The temperature. remains constant whether the expansion is tiny or huge. Heat Energy is tiny or huge right along with the expansion.

Similarly, the isothermal compression is constantly giving off heat, a fact remarked on by Sadi Carnot in "Reflections". A very large compression gives off a very large amount of heat, with no temperature. change.

Consequently, more than for any other engine cycle in use, neither the amount of heat or work is confined to be proportional to the temperature. drop.

A near infinite volume change requires a near infinite amount of heat, and does a near infinite amount of work, no matter how small the temperature. difference between the "hot" and "cold" reservoirs.

The "Carnot - Clapeyron - Kelvin : Work Ratio" ONLY APPLIES TO THE WORK TRANSFER CURVE. If heat is added or subtracted during volume change, the Work Ratio cannot be calculated based on temperature drop. Temperature. is not a meaningful measurement.

If you multiply the work ratio by the maximum temperature., you get a specific number, an amount of work. With the Carnot cycle, it gives the same number whether the work is 0 at 0 isothermal expansion, or infinite at infinite expansion.