The highly active, subglacial, Gr¿msv¿tn volcano is associated with a 20-mGal Bouguer gravity high and a broad magnetic low. The magnetic low roughly coincides with the gravity high, but short-wavelength magnetic highs are superimposed on the low, especially along caldera rims. Forward models of the gravity and magnetic fields show variable magnetization (0--12 A m-1) in the uppermost 1--2 km of the crust, probably reflecting differences in the proportions of crystalline rocks and hyaloclastites and variations in hydrothermal alteration. The models are consistent with, but do not require, a 10-km3 molten magma chamber in the shallow crust beneath the main caldera. Between 1.5 and 4 km depth, a dense body (&rgr;=2.95--3.0 Mg m-3) with a volume of 400 km3 is located, probably composed of gabbro. Modeling suggests that this intrusive body is nonmagnetic, which may imply that its temperature is at or above the Curie point. The distribution of geothermal activity at the glacier bed is consistent with heat extraction from this dense, hot intrusive body; it may be an important source for the presently observed geothermal heat output of 2000--4000 MW at Gr¿msv¿tn. This high heat transfer rate is difficult to reconcile with estimates of long-term heat production in an Icelandic rift zone volcano. The heat flux may be a transient phenomenon, caused by enhanced vertical permeability due to a recent caldera collapse and subsequent heat mining of the intrusive body.¿ 1997 American Geophysical Union