With extra insulation, the OCXO can heat up faster but cool off slower. This increases system gain for heating, lowers it for cooling which I think would tend to more overshoot. The heater is probably just a proportional controller, guessing it would go unstable if the OCXO was too well insulated and take forever to cool down after. It does need some heat loss.
It seems to be 3W max. and 1.25W typical. We don't know its target temperature or how stable the heat control is, you could look at current draw to see if it's stable.
I think all you really want is to shield it from drafts and sudden room temperature shifts, such as A/C blasts. Is your enclosure metal or plastic, ventilation louvers, PSU in there etc.
I didn't pay attention the the LTZ1000 thread as people there put covers and insulation over the IC, I thought to stop convection air currents or the cooling fan (in HP3458) from throwing the ref temperature around.