Flame and furnace aerosol reactors are used extensively for the synthesis of nanoparticles at high temperatures (800-2000 K), however, there is a limited understanding of the early stages of particle growth by collision at these temperatures. An experimental set-up to quantify the collisional growth rate and collisional correction factor (relative to the kinetic theory of gases) for flame synthesized TiO2 nanoparticles in the free molecular regime is described. Spherical charge-neutral nanoparticles with precise control of size are selected from a flame aerosol reactor (FLAR), and then passed through a downstream furnace reactor tube maintained at a high temperature. Initial and final particle size distributions (PSD) are measured using a scanning mobility particle sizer (SMPS), and the PSD is represented by a lognormal distribution. The general dynamic equation (GDE) for simultaneous coagulation and diffusive deposition is solved numerically for a laminar pipe flow using the method of moments. By comparing the experimental data with the model prediction, a correction factor to collisional growth rate is calculated. It was found that for particles in the size range 5-8 nm, there was significant enhancement in the collisional growth rate for TiO(2 )nanoparticles at 400 degrees C. This enhancement in growth rate decreased as temperature increased (upto 800 degrees C). The collisional correction factor values are compared to that of three existing models in the literature which predict similar trends with temperature, however, these models under-predict the value of the collisional correction factor. Reasons for these deviations from existing models are elucidated.