Draw manually a black intermediate shape and blur it, There's Blur slider in the fill coloring dialog. This can be used if the exact form isn't critical and a linear gradient isn't a must.
Inkscape's extension Generate from Path > Interpolate can make automatically several intermediate versions and by interpolating the style one gets also intermediate colors:
In the objects panel there's a group which contains the intermediate shapes + the originals (=endpaths) duplicated, if that's wanted
Smoother appearance is possible by increasing steps. Here's 30 intermediate shapes:
A few intermediate shapes can be enough if they are blurred. Unfortunately the blur spreads over the border of the bottom object, but that can be fixed by using a copy of the bottom object as clipping mask.
Warning: The interpolation result can be unpredictable if the paths have different directions or their node distributions differ radically.