Their argument is not melt down from surface heat but surface heat warming the surrounding area waters causing the observed melt from the bottom up.
They first must rule out incursions and any sub-surface heating from volcanic activity which is in its infant stage of study.
I recently saw a study done in relation to a warm Ocean current that had shifted south along the Antarctic coast. There are as many theories about this as there are misguided explanations.
The only explanation for warmer Ocean currents would be Solar radiation increasing the Earth’s water temps. There is also one theory out there that claims Sub sea Volcanism is partly to blame for the warmer water.