What do you mean by "portable"? Placing the refrigeration unit between the panels would add too much weight and where would the heat go?
I don't see any justification to rule out air cooling. The arrangement of the panels looks rather similar to the Sampson AESA, which is air cooled by airflow between the array faces:
View attachment 95307
Liquid cooling is also possible and might further reduce weight (because the radiators can be placed below the arrays at a lower height), at the cost of a more complex implementation.
Since the two arrays have quite different shape, I assume when you say size you mean area? 3/4 the area of 052D would be almost the size of SPY-1. Each of the SAMPSON arrays have 2560 T/R elements, which is less than half that of Type 052D. If the new radar indeed ends up 2/3 the size of Type 052D, the technological advances of the last 15 years (GaN) will almost certainly make it more capable than the Sampson AESA.
You have to remember that the Dual Sided array is tested on that mast on test ship 892. 892 has tested other radars before, one being the Type 382 Sea Eagle and an unknown single faced AESA used with the LY80 (export HHQ-16). There is no inner hollow shaft on these radars or on the mast that can be used as an vent tunnel. You also need a curved surface dome for the airflow, as in see the Type 052C vs. The very flat panel all liquid cooled Type 052D. It's much better to compare this new radar to the Thales NS100 or NS200 in its physical architecture even if these are single sided. See the Type 31 frigate as one of the customers of the radars. The compact liquid cooling needs to be mounted between the panels.
Also remember that this is the bigger brother of another dual sided AESA that already went into service on the Type 075. They should be physically and mechanically similar, except for the size and frequency of the modules. I expect both radars to be on the 054B, the same way the 054A has the Type 382 and Type 364 pairing.