Abstract We report surface displacements and gravity changes triggered by thermal modulation of shallow‐seated (∼ ${\sim} $2 km depth) silicic magma lenses during drilling. 2D plane strain models predict ground subsidence of up to 20 cm and net gravity increases of up to 82 μ $\mu $Gal from the thermal contraction of a thin (0.01 aspect ratio) sheet aligned either vertically or horizontally upon rapid (period of months) cooling from magmatic to subcritical temperatures. Application of the models in 2.5D to Krafla caldera (Iceland) where magma was encountered during drilling predicts between < ${< } $0.1 and 15 cm of ground subsidence and between 7 and 40 μ $\mu $Gal of net gravity increase during cooling of the Icelandic deep drilling project well when 0.35×106 $0.35\times 1{0}^{6}$ m3 ${\mathrm{m}}^{3}$ of coolant (1–7 vol‐% of the modeled reservoirs) were lost to the subsurface over a period of 4.5 months. We highlight the importance of magma residence time and thermal fracturing on the efficacy of thermal modulation.