Thank you Vitaliy! And yes are correct, we can do a double-dendrogram plot:
HeatmapPlot[Transpose[Rest /@ sdata[[3 ;; -1]]],
Map[Row[{"temp:", Style[#[[1]], Bold, Purple], ", lux:", Style[#[[2]], Bold, Purple]}] &, Transpose[Rest /@ sdata[[1 ;; 2]]]],
First /@ sdata[[3 ;; -1]],
DistanceFunction -> {EuclideanDistance, EuclideanDistance},
Dendrogram -> {True, True}, ImageSize -> 1000]

This plot seems more informative than the first one I posted. Note the grouping of the temperature and lux pairs becomes the same as in the raw data.