Bottom "heat" pattern is definately IR reflection on the gold plated circular shape.
I since I didn't build any LTZs lately, must not resist the urge to build few more, this time bit different, and more traditional design to discuss about.
PNG-schematics
The LTZ1000 part looks very conventional. I somewhat doubt one would really need 0.2 ppm/K resistors. The important parameter on the resistors should be long term stability, not the TC. Of cause they usually come together, but not always. Just for the TC the resistors look better than needed. Due to the high current output a transistor the LT1013's output might be a good idea, though not absolutely needed.
For the voltage regular, one usually needs the capacitors just at the input and output of the regulator, even close by. So even just a ferrite bead as shown could make the regulator oscillate. Extra inductive filtering should be on the input side and maybe after the first set of capacitors at the output. If you really want the LTC2057 in the circuit, I would use a separate regulator (even if just an 78L15), as the 2057 would be a significant source of RF noise. One might also want some filtering between the LTZ reference an an AZ op at its output.
The 7 to 10 V circuit shown does not look like it would tolerate capacitive loading and could compensate for voltage drop at the GND side. Not sure with this, as the drawing is a little confusing. The resistors in the 7 to 10 V part are way more critical (e.g. a factor 100) than in the LTZ1000 part. So one should also have an direct output at the 7 V level so one could at least check for long time drift of the resistor ratio.
The divider might also need resistors for trimming, if exactly 10 V are intended.
Due to the errors expected from the resistors in the 7 to 10 V stage one might consider a good conventional OP instead of a AZ type. This might need slightly lower resistor values however.