Trimerization of formaldehyde can happen at high temperatures, but appear to require catalysts. There is a patent for synthesizing 1,3,5-trioxide at high temperature. This patent uses phosphoric acid catalysts.
According to the patent:
The process of the invention is advantageously carried out at reaction temperatures of from 80 to 160° C., preferably from 90 to 145° C., at an inlet partial pressure of the formaldehyde of from 0.5 to 5 bar absolute, preferably from 0.5 to 2 bar, and at an inlet concentration of formaldehyde of from 1 to 100% by volume, preferably from 20 to 100% by volume
There is also an early study which explored the kinetics of the reaction but for a different catalyst. In "Vapour-phase trimerization of formaldehyde to trioxane catalysed by 1-vanado-11-molybdophosphoric acid" by Kern and Emig, they use a molybdophosphoric acid catalyst. They used a tube reactor and varied the temperature from
102.5 to 110° C. According to their study:
The
conversion
observed
increases
extremely
with
decreasing
temperature.
However, they comment that
the
temperature
dependence
cannot
be
attributed
to
thermodynamic
effects
only.
It
has
to
be
related
to
the
properties
of
the
heteropoly
compound.
Another study is "Synthesis of Trioxane Using Heteropolyacids as
Catalysts" by Mazamoto et al. Their process uses heteropolyacids as catalysts and they were able to obtain a conversion % of 22.9 at 110° C. Where
$$\text{Conversion %}=\frac{3[\text{trioxane}]+2[\text{methyl formate}]+[\text{methylal}]}{[\text{feed formaldehyde}]}\cdot 100$$