## 1 Introduction  
In the last decades, photothermal research, developments, and applications have been the object of intense activity [1; 2], with particular emphasis on the scope of photothermal therapy (PTT). The local heat source produced by nanoabsorbers in the near-infrared region (NIR) has revealed a new and promising non-invasive therapeutic area. The thermal ablation consists in producing local heat, through the illumination of nanoparticles, in order to destroy the tumoral cell [3; 4; 5; 6; 7]. Such nanoparticles (or agglomerations of nanoparticles with complex shapes) form photothermal agents (PA). The main specificity of such therapies in NIR regime are to treat very local tumor cells and preserve the surrounding tissues [8; 9; 10]. Indeed, NIR light (650-950 nm) induces minimal absorption by skin and tissue, leading to minimal tissue invasion and deeper tissue penetration (up to 10 cm). A laser illumination is absorbed by the PA, producing a local temperature elevation. Such a temperature elevation depends on the material, the shape, and the size of the PA, but also on the distance between the nanoparticles. These local heat sources are expected to satisfy two conditions: first, they will overpass the thermal ablation threshold within a range of a reasonable maximum temperature limit; second, they will avoid exceeding the thermal ablation temperature outside the treated biological media/cells (or the target cancer cells). Such a control of the temperature is essential.  
For a specific cancer cell, the only difference is not directly on the temperature elevation as a function of the agglomeration of nanoparticles, but on the material functionalization (or the functionalization of individual nanoparticles) improving the binding to the cancer cell [11; 12; 13; 14]. In vitro, that consists in a transfection of the nanoparticles to cancer cells before the internalization of the nanoparticles in the cancer cells. In vivo, the nanoparticles are injected intravenously or intratumorally before migrating to the tumor or cancer cells [15].  
This theoretical study focus on the process of temperature elevation above the ablation threshold (and under a limit of maximum temperature) as function of the nanoparticles concentration in a generic biological medium/cell. Here, we compute and analyze the spatial evolution of the temperature around agglomerations of nanoparticles in a range of parameters (the shape and size of the agglomerates, and the diameters and concentration of the nanoparticles) [16; 17]. Therefore, we obtain a range of concentrations of particles, satisfying both the constraints of efficiency of PA and limiting the risk for the surrounding media/cells. The computation of the temperature elevation induced by a single nanoparticle and electromagnetically coupled agglomerates in a biological media or cell are achieved through the finite element method (FEM). The weak-coupled electromagnetic and heat partial differential equations are solved by using a 3D adaptive remeshing scheme with an error estimator controlling the accuracy of the numerical solutions in the multiscale domain of computation [18; 19; 20; 21]. Statistical analysis of the temperatures produced from random positions of nanoparticles reveals the domain of an adequate concentration of nanoparticles.  
The organization of the paper is as follows. In Section 2, we present the main equations, the physics parameters, and the numerical method (details are given in Appendices A.1 and A.2). In Section 3, we show the simulation results and discuss the effects of the mass concentration and of the agglomerate configurations and, therefore, on the temperature elevation before concluding.