In an embodiment, a processor includes a first chip of a multi-chip package (MCP). The first chip includes at least one core and first chip temperature control (TC) logic to assert a first power adjustment signal at a second chip of the MCP responsive to an indication that a first chip temperature of the first chip exceeds a first threshold. The processor also includes a conduit that includes a bi-directional pin to couple the first chip to the second chip within the MCP. The conduit is to transport the first power adjustment signal from the first chip to the second chip and the first power adjustment signal is to cause an adjustment of a second chip power consumption of the second chip. Other embodiments are described and claimed.