As far as I remember, I first heard Tempus Est Iocundum performed by Philip Pickett & the New London Consort in the early/mid 1980s, & later bought the album (Carmina Burana Volume 1) which I still have. Oddly enough, The Clemencic Consort's exhaustive 5 album set of Carmina Burana originals (mid 1970s) omits TEI, but remains something of a benchmark in the interpretation of Mediaeval song, along with their sets of Cantigas de Santa Maria & Troubadours etc. - in all cases the presence of idiosyncratic hurdy-gurdy maestro & singer Rene Zosso adds to the hoary darkness of the music! Nice to see him turning up on the new Hesperion XXI Estampies & Danses Royales disk. The NAXOS Unicorn / Wytars disk is good, with members coming up through The Clemencic Consort; and there are, literally, dozens of others that I've never heard. There's a very interesting version on YouTube somewhere too.

The tune I use I actually got from performing with musicians from Durham University in the early 1990s, as well as working with musicians from the Schola Cantorum Baliensis, so I've never questioned the general consensus on the melody, although variations, of course, do exist. I also performed & recorded it with the mediaeval group Misercordia pretty much with that melody, although the organum voicings & translation passages are entirely improvised in the spirit of the seminal influences in such matters.