## 1 Introduction  
Dental implant bed preparation consists in drilling a hole in the alveolar bone at the target site. This process results in heat generation due to bone deformation next to the cutting edge of the drill and friction between the drill's cutting tip and the underlying bone [1]. The amount of heat dissipated in the adjacent bone depends on several factors, including bone density, drilling speed, applied thrust force, drill parameters (material, design, diameter, and wear [2]), drilling procedure, and irrigation conditions (coolant fluid flow rate and temperature) [3]. Overheating can lead to irreversible bone damage, poor osseous integration of the implant, and, eventually, implant failure [4]. Therefore, the thermodynamics of osteotomy is an active field of biomedical research, with important milestones and several open questions [5; 6; 7]. The biological impact of temperature elevations caused by surgical drilling depends on the thermal history of the heated bone, not just on its peak temperature [8]. Intravital microscopy experiments conducted on rabbit tibia indicated that a temperature increment of 10 \({}^{\circ}\)C maintained for one minute did not lead to significant bone resorption. However, capillaries dilate for about 5 days, during which some fat cells in the heated area die. With five minutes of exposure, 20-30% of bone tissue is resorbed and replaced by fat cells within a month. Heating bone to 50 \({}^{\circ}\)C for one minute kills most fat cells, leading to a 30% loss of bone [9]. Therefore, for heat exposures that last up to one minute, 47 \({}^{\circ}\)C is considered the threshold temperature for bone tissue damage [10]. This estimate aligns well with the outcome of an in vivo study conducted on adult patients who received osteectomies for maxillary dental implant placement. The distribution of apoptotic osteocytes around the osteotomy was compared with the calculated temperature field, and the results indicated a threshold temperature for osteocyte death of about 47 \({}^{\circ}\)C [5]. Dental implant bed preparation can be performed manually, in an open-flap procedure (whereby the soft tissue is temporarily peeled off the underlying bone), or in a guided, flapless manner (whereby a surgical guide is placed over the target site and the drill passes through a sleeve that controls its position and orientation during osteotomy). Flapless guided surgery is the fastest, most accurate, and least traumatic procedure [11; 12; 13], but it entails the most bone heating [14]. Indeed, a classical surgical guide, composed of a personalized splint outfitted with a cylindrical sleeve, shields the target site and deviates the irrigation fluid jet from the drill's point of entry. The first quantitative study of the impact of surgical guides on bone heating in the course of implant bed preparation was conducted by [PERSON] et al. on bovine femoral cortical bone samples [15]. Their results confirmed the hypothesis that more heat is generated in guided osteotomy than in the free-hand approach. Although the differences between mean maximum temperatures were statistically significant, they remained within the safe zone (below 47 \({}^{\circ}\)C) [15]. These findings are encouraging, since the cortical layer of the bovine femur is thicker and denser than that of the human mandible [16], and, therefore, even less temperature elevation is expected in a clinical context. Nevertheless, further research is warranted because individual temperature rises might exceed the safety threshold. Furthermore, circulation also contributes to heat exchange in a living organism. In their in vivo rabbit tibia study, [PERSON] et al. [17] reported a mean peak temperature of 31.8 \({}^{\circ}\)C (28.5 \({}^{\circ}\)C) and individual temperatures below 34.6 \({}^{\circ}\)C (30.5 \({}^{\circ}\)C) when 40 drillings were performed with (without) a surgical guide. Also, the in vitro study conducted by [PERSON] et al.