The OEM FH012 and the SH847 have different temperature signatures because they operate completely differently and with different types of power components
The OEM is a MOSFET Shunt device and is actually running at much higher current; however MOSFETs have extremely low 'on' resistance, so even though the current is high, the dissipated power is quite low (power = I^2*R)
The SH847 is a Series Regulator - those Series components will actually run at a much lower current; (I am not sure what type of devices are actually in these modules but I believe they are SCR's); it probably runs about half the current that the MOSFET unit will;
so there is an advantage there from the current, however the resistance is higher.
So the SH847 wil tend to get a bit hotter than the MOSFET Shunt unit will, even though the operating current is lower
But note that is has a significantly bigger heatsink, with larger cooling fins; so even modest airflow will help to dissipate the generated heat (it will still dissipate heat even with out a physical flow across it)
The primary difference in operation is that the MOSFET is ALWAYS conducting max current; so its temperature is going to be solely determined by how fast the engine is turning (higher rpm means more current generated - but only up to a max at about maybe 3k rpm) and how much heat it gives up;
the Series will conduct only as much current as is being demanded by 'the load' (the sum of all the circuits demands); so it will operate hotter (respectively, not necessarily 'HOT') with say, the aux lights on, than not.
It will make little to no difference how fast the engine is turning in its case; so at higher rpm (say cruising) its relative power dissipation will be the same as at idle.
Note also that with a Shunt Regulator, reducing the bike's load with say, LED lights will make zero difference in reducing its temperature - indeed to the contrary, if you turned the lights off altogether, the Shunt device is actually going to get HOTTER! (because it has to shunt even more current to make up for what the bike is not consuming);
However with a Series R/R, reducing that bikes load (e.g. LED headlight and aux lights) will actually mean less current conducted through the R/R so will indeed actually run cooler than with std components.
I would have thought there would not be a significant difference whichever way round it was mounted in that location.
The simple test is to go on a good ride and check the temp when you get back;
You could also run it at idle with zero air-flow over it and see how hot it gets in that condition.
I did that test with mine (bike static) and the temperature rise was not excessive.
My bike runs similar load to a Std/Roadster, with twin headlights; the Touring (with single headlight) is running less load (not accounting for any accessories that may be on)
Note that in your respective cases, you cannot simply compare the temp of one vs the other (for fins facing in or out in approx same location) - you have to also know that the load on each is the same. i.e. if one of you has LED lights and the other std, it will make a difference.