No you can't. Thermal properties and surface thermodynamic properties can be determined by DSC, DTA but for size determination you will have to perform TEM, SEM, dynamic light scattering (DLS) electrophoretic light scattering , SPR (plasmon resonance), nanoparticles tracking analysis (NTA)....
@ Gills Dollo- Thank you for the answer sir. DO thermal properties as well as the surface thermodynamics changes as we go small in the size? Is there any hierarchy ? If yes then Can't we relate it with the size?
Yes you are right, surface thermodynamics properties (molar surface energy, molar surface entropy and molar surface enthalpy) have been shown to increase when the size of nanoparticles decrease (see references below) but it may be difficult to obtain precisely the size with these indirect methods , and it is so easy and quick with DLS...
Wenjiao Li, Yongqiang Xue, Zixiang Cui. Dependence of surface thermodynamic properties of nanoparticles and its determination method by reaction rate constant; Physica B: Condensed Matter; Volume 495, 15 August 2016, Pages 98–105
Meng Wang,Jinhua zhu,Yongqiang Xue,Zixiang Cui, Miaozhi Zhao. Size-dependent surface thermodynamic properties of silver oxide nanoparticles studied by electrochemical method; Journal of Materials Science;January 2017, Volume 52, Issue 2, pp 1039–1046