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Non-invasive geophysical prospecting and a thermodynamic model were used to examine the structure, depth and lateral extent of the frozen core of a palsa near Lake Peeraj\"arvi, in northwest Finland. A simple thermodynamic model verified that the current climatic conditions in the study area allow sustainable palsa development. A ground penetrating radar (GPR) survey of the palsa under both winter and summer conditions revealed its internal structure and the size of its frozen core. GPR imaging in summer detected the upper peat/core boundary, and imaging in winter detected a deep reflector that probably represents the lower core boundary. This indicates that only a combined summer and winter GPR survey completely reveals the lateral and vertical extent of the frozen core of the palsa. The core underlies the active layer at a depth of ~0.6 m and extends to about 4 m depth. Its lateral extent is ~15 m x ~30 m. The presence of the frozen core could also be traced as minima in surface temperature and ground conductivity measurements. These field methods and thermodynamic models can be utilized in studies of climate impact on Arctic wetlands.