Why is LUVOIR actively heated?
The main reason appears to be to prevent any icing up and contamination of the mirrors and other optical coponents with water and other "non-volatile residues", which would be extremely detrimental to the UV performance.

Emissivity at 270K is not too much of an issue since the instrument only works out to 2 microns.

The issue is briefly discussed in section 8.1.10 of the LUVOIR final report.