Due to the large variety of possible clinical scenarios, a reliable heating-risk assessment is not straightforward when patients with arthroplasty undergo MRI scans. This paper proposes a simple procedure to estimate the thermal effects induced in patients with hip, knee, or shoulder arthroplasty during MRI exams. The most representative clinical scenarios were identified by a preliminary frequency analysis, based on clinical service databases, collecting MRI exams of 11,658 implant carrier patients. The thermal effects produced by radiofrequency and switching gradient fields were investigated through 588 numerical simulations performed on an ASTM-like phantom, considering four prostheses, two static field values, seven MR sequences, and seven regions of imaging. The risk assessment was inspired by standards for radiofrequency fields and by scientific studies for gradient fields. Three risk tiers were defined for the radiofrequency, in terms of whole-body and local SAR averages, and for GC fields, in terms of temperature elevation. Only 50 out of 588 scenarios require some caution to be managed. Results showed that the whole-body SAR is not a self-reliant safety parameter for patients with metallic implants. The proposed numerical procedure can be easily extended to any other scenario, including the use of detailed anatomical models.