To answer the growing demand for hardware acceleration, Amazon, Microsoft, and many other major cloud service providers have included field-programmable gate arrays (FPGAs) in their datacenters. However, researchers have shown that cloud FPGAs, when shared between multiple tenants, face the threat of remote power side-channel analysis (SCA) attacks. FPGA time-to-digital converter (TDC) sensors enable adversaries to sense voltage fluctuations and, in turn, break cryptographic implementations or extract confidential information with the help of machine learning (ML). The operating temperature of the TDC sensor affects the traces it acquires, but its impact on the success of remote power SCA attacks has largely been ignored in literature. This paper attempts to fill in this gap. We focus on two attack scenarios: correlation power analysis (CPA) and ML-based profiling attacks. We show that the temperature impacts the success of the remote power SCA attacks: with the ambient temperature increasing, the success rate of the CPA attack decreases. In-depth analysis reveals that TDC sensor measurements suffer from temperature dependent effects, which, if ignored, can lead to misleading and overly optimistic results of ML-based profiling attacks. We evaluate and stress the importance of following power side-channel trace acquisition guidelines for minimizing the temperature effects and, consequently, obtaining a more realistic measure of success for remote ML-based profiling attacks.