A multi-processor kernel will not (in itself) affect CPU temp
Running a multi-processor kernel vs. a single-processor kernel will not affect your CPU temps in itself. The key difference between the kernels is that the multi-processor kernel contains additional code to synchronize access to shared kernal data (since you may have two or more processor threads running concurrently).
Consequently, running a multi-processor kernel on a single-processor system is *slightly* slower (i.e., less efficient) than running a single-processor kernel that does not contain extra synchronization code you don't need. However, the extra overhead of an MP kernel is very small when compared to total CPU power; any affect on the temperature is negligible.
In the example cited, it is far more likely that the new single-core CPU that the user installed simply runs hotter than the dual-core it replaced. For example, my 3500+ Clawhammer (130 nm) CPU overclocked to 2.4GHz ran at 58C under full load. My new dual-core X2 4400+, however, runs at 48C under load overclocked at 2.4GHz. The temperature difference has nothing to do with which kernel I am running -- Athlon 130 nm chips simply run hotter than 90 nm chips.