We present an exploratory numerical model for the thermal evolution and fragmentation of pristine interstellar comets during a first passage through the inner Solar System, and we apply it across a grid of perihelion distances (q=0.25–1.5~AU) and tensile strengths (σ_t=50–500~Pa). The model follows a single nucleus (M_0=2\times10^{12}~kg, R_0\approx1060~m, dust/ice =1, ice composition 35% CO, 30% CO_2, 15% CH_4, 20% H_2O) along a continuous hyperbolic trajectory, solving heat conduction into an initially 30~K interior, energy-balanced multi-species sublimation with retreating volatile fronts, dust lifting and lag-mantle growth, and a subsurface gas-pressure failure criterion, so that the number of fragments is an emergent outcome rather than a numerical input. In our primary case (q=1~AU, σ_t=100~Pa) the nucleus begins splitting essentially at the 3~AU start of the simulation (~2.99~AU within the first day), as soon as a sub-millimeter lag deposit partially confines the warming CO front—implying that for pristine composition the onset lies beyond our starting distance—and disaggregates through 63 binary splittings into at least 64 fragments—our tracking cap, reached near perihelion after a self-limited pre-perihelion plateau at 53 bodies—with 1.3% total mass loss; sublimation is energy-limited, so reservoir depletions stay modest (CO 2%, CH_4 2%, CO_2 1%, H_2O <0.1%) and the shattered body retains almost all of its mass as a fragment swarm; the mass budget closes to machine precision. Across the explored grid, no combination leaves the nucleus intact, and mass loss depends only weakly on q and σ_t (0.8–1.7%) while depending strongly on composition: depleted, 67P-like ices reduce mass loss to 0.1% at q=1~AU.

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