Answer Description

Since the offset is inconsistent and the clock issues seem to revolve around the system not being powered on it could be a CMOS battery issue. If it were an NTP (port 123) or timezone issue you would likely see a consistent offset. None of these symptoms are typical of an overheating system.

Wikipedia

Nonvolatile BIOS memory refers to a small memory on PC motherboards that is used to store BIOS settings. It is traditionally called CMOS RAM because it uses a volatile, low-power complementary metal–oxide–semiconductor (CMOS) SRAM (such as the Motorola MC146818 or similar) powered by a small "CMOS" battery when system and standby power is off. It is referred to as non-volatile memory or NVRAM because, after the system loses power, it does retain state by virtue of the CMOS battery. The typical NVRAM capacity is 256 bytes.The CMOS RAM and the real-time clock have been integrated as a part of the southbridge chipset and it may not be a standalone chip on modern motherboards. In turn, the southbridge have been integrated into a single Platform Controller Hub. Today's UEFI motherboards use NVRAM to store configuration data (NVRAM is a part of the UEFI flash ROM), but by many OEMs' design, the UEFI settings are still lost if the CMOS battery fails.