We haven't found any specific information regarding TME to BR4 conversion on internet. However both these file types originate from Bryce graphics software and if any program can somehow convert / export both of these files, it would be it.
Convert Bryce animation time curve file to Bryce version 4 scene.
We found 2 software records in the database related to .tme to .br4 file format conversion.
Microsoft Windows software - convert tme to br4 on Windows
A graphics design tool for making 3D landscaping and animations
Convert from tme file format
The tables with software actions are a good pointer for what a certain program does with various file types and often may give users a good hint how to perform certain file conversion, for example the above-mentioned tme to br4. However, it is not perfect and sometimes can show results which are not really usable because of how certain programs work with files and the possible conversion is thus actually not possible at all.
Apple macOS / Mac OS X software - convert tme to br4 on OS X
3D modeling and animation package for Mac.