You’re right that in heat capaity measurements heat leaks are always a major worry. They aren’t especially different for water or other liquids, such as common oils.
Once you’ve got a fairly good thermos, there are several things you can do to minimize the heat leaks and to estimate and correct for them. For example, let’s say that you want to measure the heat capacity of some water near 30°C, maybe by seeing how much energy you had to put in to heat from 25°C to 35°C. You could pre-warm the whole thermos to 30° C before adding the water, so that the heat leaks in at the beginning would nearly cancel the heat leaks out at the end. It also helps to run the heater at a high intensity, so that the time required is short.
You can also carefully measure how the temperature changes with time when you have no deliberate heat input. That gives a background to subtract from whatever changes ocur when you have a heat input. Of course the background will depend on both the water temperature and the thermos temperature.
There will also be some heat capacity of the heater itself. You can check for its effects by seeing how the effective heat capacity depends on the water volume. It's only the change with water volume that counts, since for small volumes the heater is a big part.
One other factor to consider is that evaporation will reduce the temperature. You can figure out the size of that effect by measuring the amount of water before and after the experiment. You also need to know the latent heat of vaporization, but you can measure that too by seeing how much heat is needed to boil off a given amount of water starting at 100°C. Evaporation will probably be a bigger problem for alcohol, but a maller problem for oil.
Once you correct for these effects, i bet you can measure the heat capacity to better than 10% accuracy without much trouble.
(published on 10/22/2007)