Tests have to be performed to rule out proposals for gravity modification. We propose a new idea for constraining alternative theories of gravity using temperature-dependent white dwarf (WD) mass-radius (MR) observational data. We have shown that several alternatives to general relativity (GR), which modified GR only within matter, might be reduced to the well-known Poisson equation similar to that of Eddington-inspired Born Infeld (EiBI) and Minimal Exponential Measure (MEMe) gravity. Retaining EiBI notation, we constrain the value of the coupling constant, κ , using a high-precision model-independent measurement of WD MR observations. We have demonstrated that the WD model should include detailed physics to achieve good precision. The model should include their temperature and evolutionary aspects, which may be computationally expensive. To overcome this issue, we construct a semi-analytical surrogate model based on Mestel’s model, calibrated with tabulated, detailed realistic models, to correct the zero-temperature radius. We have shown that the best-fit value of κ depends on the WD model, with the ’thick’ envelope models more consistent in describing data. The tightest bound obtained from the most precise MR measurement, QS Vir, with - 0.19 ≲ κ≲ 0.22 in 10 3 m 5 kg - 1 s - 2 for 2 σ(∼ 95 %) credibility. Overall, we assert that the recent precise WD MR measurements, combined with our current understanding of WD structure, are insufficient to see the deviation from the one predicted by GR. Both more precise observation data and detailed WD modelling are required to rule out gravity modification.