What is the difference between irreversible and reversible isochoric processes done on an ideal monatomic gas in a frictionless system?

Suppose we had two thermal reservoirs at $T_{c}$ and $T_{h}$ with $T_{c} < T_{h}$ and an infinite series of thermal reservoirs with a continuous range of temperatures between $T_{c}$ and $T_{h}$.

Now consider an isolated system containing these thermal reservoirs and a frictionless rigid container filled with an ideal monatomic gas at a temperature of $T_{c}$.

If we heat this system isochorically there are two options:

1. We use the infinite thermal reservoirs to heat the system reversibly.
2. We use the two thermal reservoirs to heat the system irreversibly.

In case 1. we have $Delta W_{text{rev}}=0$ and $Delta Q_{text{rev}}=frac{3}{2}Nk_{text{B}}Delta T$ but what about case 2? What would $Delta W_{text{irrev}}$ and $Delta Q_{text{irrev}}$ be?

I know there are other types of work to consider in the irreversible case (non-$PDelta V$ work), but do any of these apply to this system?