We investigate the accessibility of Ti3SiC2-derived carbons (Ti3SiC2-DCs) synthesized non-isothermally using a temperature ramp. The microstructure of the Ti3SiC2-DCs is characterized using TEM, XRD, Raman spectroscopy and gas adsorption. For the characterization by gas adsorption, we adopt our Finite Wall Thickness (FWT) model to invert Ar adsorption isotherms at 87K to obtain pore size and pore wall thickness distributions of the Ti3SiC2-DCs. Accordingly, we identify a pore accessibility problem in the Ti3SiC2-DCs, as reported for Ti3SiC2-DCs prepared at 1073K in our previous work. A striking feature is that Ti3SiC2-DC prepared at the slowest ramping rate (2K/min) has a very narrow pore size distribution, while the Ti3SiC2-DCs synthesized at higher ramping rates (5 and 15K/min) have much broader pore size distributions centered around 5.2Å. A significant amount of previously unreported ultra-microporosity is observed based on low pressure CO2 adsorption at 273K. Our results indicate that slow ramping rate could potentially be utilized for fine control of the ultra-microporosity of carbide-derived carbons. Finally, we have found that fast ramping rate above 5K/min leads to subtle changes in microstructure, with long and periodic graphitic multilayers having some large pores formed in between.