> 1) I’m reluctant to embrace Paul Pukite’s models that couple the Earth’s heat energy to its rotational energy.
Much as I would like to take credit for it, that is not my model. What Dickey et al observed  and Lambeck&Cazenave well before that  is that long-term variations in either the core angular monentum (CAM) or length-of-day (LOD) map well to variations in the global average temperature.
"The continued correlation of the corrected temperatures with Earth rotation variations after this time underscores the significance and size of the anthropogenic effect on SAT and implies that the observed temperature cannot be the cause of the correlated variation in Earth rotation but rather that both are instead influenced by an external cause (Lambeck and Cazenave 1976). Note an approximately 8-yr lag between the (negative) LOD and the corrected temperature; this lag agrees with the 8-yr lag between changes in Earth’s rotational speed and surface geomagnetic field perturbations found by Roberts et al. (2007)."
The following is a comparison to a temperature model, but a similar match occurs with the actual GISS temperature data.
The more rapid variation on top of the long-range variation is a combination of ENSO and volcanic activity.
So even though this is not my model, I will apply it as a proxy for the unknown origin long-range temperature variations that arise. I suppose that is aggressive on my part, but if nothing else, it works well as a heuristic. But this really has nothing to do with the ENSO or El Nino behavior which is of shorter term variability. The only reason that I engaged in the discussion is that nad brought it up.
 Dickey, Jean O., Steven L. Marcus, and Olivier de Viron. "Air temperature and anthropogenic forcing: insights from the solid earth." Journal of Climate 24.2 (2011): 569-574.
 Lambeck, Kurt, and Amy Cazenave. "Long term variations in the length of day and climatic change." Geophysical Journal International 46.3 (1976): 555-573.
> 2) I’ve been reluctant to embrace Nadja Kutz’s theory that an exact biannual cycle in the Earth’s temperature could arise from a resonance of the magnetic fields of Earth and Sun.
The biannual cycle is a actually pretty straightforward to explain. The sun crosses the equator twice each calendar year. One time exposing the northern hemisphere with more solar energy , and the other time exposing the southern hemisphere more. This leads to a biannual harmonic in the temperature time series.