Temperature changes in the vicinity of a single absorptive nanostructure caused by local heating have strong implications in technologies such as integrated electronics or biomedicine. Herein, the temperature changes in the vicinity of a single optically trapped spherical Au nanoparticle encapsulated in a thermo-responsive poly(N-isopropylacrylamide) shell (Au@pNIPAM) are studied in detail. Individual beads are trapped in a counter-propagating optical tweezers setup at various laser powers, which allows the overall particle size to be tuned through the phase transition of the thermo-responsive shell. The experimentally obtained sizes measured at different irradiation powers are compared with average size values obtained by dynamic light scattering (DLS) from an ensemble of beads at different temperatures. The size range and the tendency to shrink upon increasing the laser power in the optical trap or by increasing the temperature for DLS agree with reasonable accuracy for both approaches. Discrepancies are evaluated by means of simple models accounting for variations in the thermal conductivity of the polymer, the viscosity of the aqueous solution and the absorption cross section of the coated Au nanoparticle. These results show that these parameters must be taken into account when considering local laser heating experiments in aqueous solution at the nanoscale. Analysis of the stability of the Au@pNIPAM particles in the trap is also theoretically carried out for different particle sizes.