That was just to give you an idea on how to do a 2 sided, PCB with all components on 1 side,
The traces can be nudged to get some good via coupling to the VEE pins (-2.5V on the schematic), To the same extent the -2.5V connection to the capactors and similar could be made much thicker to pull some heat with them
At 38C/W, and what reads as about 0.25W of dissipation from the datasheet, I cant see where there is much need for over the top PCB cooling.
Edit:
Part of the extra heating your seeing there is from the ones on the back, Ironically by making it on the same side, the density of the heat sources would be lower.
Edit2: Here is what you could do if you wanted some extra heat sinking.
Edit3: Just to make clear, at this point I have put 0 effort into impedance matching, If you guys need help with it, I would just need to know what board thickness your working towards.