@Joey Hess @IBob
Here is the spec's sheet on the PCM materials. The A4 has a Latent heat capacity of 200 kJ/kg (water is 334 kJ/kg) and a specific heat of 2.18 kJ/(kg⋅K) (water is 4.19 kJ/(kg⋅K)). Generic vegetable oil having a specific heat range from 1.67 - 2 kJ/kg.
From this source, the latent heat capacity of peanut oil is 21.7 cal/g which is 90.8 kJ/(kg⋅K) which is half of that of water. Although, oils often melt over gradually over instead of at one eutectic point, so it's possible that a decent amount of thermal energy is stored in the range (note it's a per deg K change rate). This document gives examples of this phenomena in usage for cooling systems.