Analytical solutions are much less computationally intensive than numerical ones, and moreover, they are more accurate because they do not contain numerical errors; however, they can only describe a small group of simple heat-conduction problems. A numerical simulation of heat conduction is often used as it is able to describe complex problems, but its computational time is much longer, especially for unsteady multidimensional models with temperature-dependent material properties. After a discretization using the implicit scheme, the heat-conduction problem can be described with N non-linear equations, where N is the large number of the elements of the discretized model. This set of equations can be efficiently solved with an iteration of the line-by-line method, based on the heat-flux superposition, although the computational procedure is strictly serial. This means that no parallel computation can be done, which is strictly required when a graphics card is used to accelerate the computation. This paper describes a multidimensional numerical model of unsteady heat conduction solved with the line-by-line method and a modification of this method for a highly parallel computation. An enormous increase in the speed is demonstrated for the modified line-by-line method accelerated on the graphics card, and the durations of the computations for various mesh sizes are compared with the original line-by-line method. Keywords: heat conduction, numerical simulation, multidimensional numerical model algorithm, acceleration, parallelization, graphics card Analiti~ne re{itve so mnogo manj ra~unsko intenzivne kot numeri~ne, poleg tega pa so bolj natan~ne, ker ne vsebujejo numeri~nih napak, vendar pa lahko opisujejo samo majhno skupino enostavnih problemov prevajanja toplote. Numeri~na simulacija prevajanja toplote se pogosto uporablja, ker je sposobna opisati kompleksne probleme, vendar pa je~as izra~una mnogo dalj{i, {e posebno pri nestabilnih ve~dimenzijskih modelih, z lastnostmi materiala, odvisnimi od temperature. Po diskretizaciji z uporabo implicitne sheme je mogo~e problem prevajanja toplote opisati z N nelinearnimi ena~bami, kjer je N veliko {tevilo elementov diskretiziranega modela. Ta sklop ena~b je mogo~e u~inkovito re{iti s pribli`kom metode vrsta za vrsto, ki temelji na predpostavki toka toplote,~eprav izra~un poteka serijsko. To pomeni, da ni mogo~vzporedni izra~un, kar je striktna zahteva, kadar se uporablja grafi~no kartico za pohitritev izra~una. Ta~lanek opisuje ve~dimenzijski numeri~ni model nestabilnega prevajanja toplote, kar je bilo re{eno z metodo vrsta za vrsto in s pospe{itvijo modifikacije te metode na grafi~ni kartici. Trajanje izra~una je primerjano z osnovno metodo vrsta za vrsto pri razli~nih dimenzijah mre`e.