Thermal diffusion and measurement noise can obscure the number and individual parameters of localized heat sources. We study the reconstruction of constant positive point sources from temperature histories at a few sensors, without prescribing the source count. Orthogonal matching pursuit or least angle regression selects candidate locations from a unit-response dictionary. These candidates initialize continuous constrained fits, and a noise-based discrepancy rule selects the smallest accepted model among the attempted fits. The response analysis distinguishes rejection of a merged one-source model from accurate recovery of the individual sources. It gives a projected quadratic residual for a close pair, a weak direction in the two-source parameters, and a conditional bound for recovering the total strength and strength-weighted center of an unresolved cluster. A local Gaussian approximation relates one-source rejection to noise and separation. Paired numerical tests compare sensor and time-sampling budgets, noise levels, and source separations. Finite-plate data generated independently of the inverse response and a three-dimensional example assess the same fitting procedure. In the tested configurations, source-count selection and individual parameter recovery differ substantially, while unresolved pairs can retain accurate aggregate estimates. The framework combines reconstruction with a local interpretation of which heat-source information the observations support.

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