Here they supposedly measured a flame temperature between 124 and 144 °C, but it's a technical report from a company which sells oxyhydrogen (so-called "HHO") systems:
It will take a bit to work through what is claimed in this paper.
There are substantial amounts of data available for download for this paper. The author is highly commended on that. The calculation spreadsheets are actually available.
One thing that is apparent is that only one state of H and O are considered, just 1/3 O2 and 2/3 H2. OH is neglected.
There is no laser wavelength refraction adjustment for atmosphere, but that is possibly negligible.
There is an extra table showing an emissivity-temperature re-calculation. It appears to show an IR spot size larger than the flame width. A wiki link and a reference to the emissivity of copper is mysteriously supplied.