Fabrication methods for low-density fine-structure (cell size < 1 m) 3-D networks of cellulose triacetate (TAC) are developed. Target densities ranged 4-20 mg/cm3, similar polymer structures were produced both with no load and with high-Z cluster dopant with concentration up to 30%. Foams of varying density down to 0.25 plasma critical density at the third harmonic of iodine laser wavelength are supplied for laser shots. Closed-cell and 3-D network structures are considered and monitored as the means of thermal and radiation control in plasma. In comparative foam-and-foil laser irradiation experiments on PALS (Czech, Prague) laser facility the presently developed TAC targets were used along with earlier reported TMPTA (trimethylol propane triacrilate) and agar foams. Radiation transport and hydrodynamic wave velocities proved to be similar in TAC and TMPTA volume structures both having the form of regular 3-D networks, but differed a lot when TAC was compared to agar foams. Radiation transport during laser pulse in TAC doped with Cu-clusters was faster then in TAC with no dopant, whereas plasma from TAC doped with Cu-clusters cooled down quicker then with no clusters. High-Z cluster dopant is effective tool to control energy transport in underdense plasma.