Products of silicate synthesis
I imagine it's called something like $\ce{Na2SiO4Mg}$.  Tomorrow I will try some combinations of sodium silicate with Aluminum Oxide, and magnesium oxide. What would these be called?


Much simplier than that. Sodium hydroxide dissolves incredibly exothermally:

$$\ce{NaOH (s) -&gt; NaOH (aq)}\qquad{\mathrm{\Delta} H = \pu{-44.5 kJ mol-1}}$$

This is what heated your mixture.