Discharges with strongly peaked density profiles, density peaking factor >4, have been produced on the Tokamak Fusion Test Reactor (TFTR) tokamak by deuterium pellet injection. Following the pellet perturbation, these plasmas have been heated using 3He or hydrogen minority ion cyclotron resonance heating (ICRH) at power levels up to 6 MW. As seen in experiments on other devices, a strong transient enhancement of the central plasma parameters, in particular of the fusion reactivity and central electron pressure, has been observed in these discharges. The transport characteristics of these plasmas during the period of enhanced core confinement have been analysed using the TRANSP time dependent interpretive code. The time evolution of the q profile is calculated and compared with measurements. The influence of plasma current and heating power is examined. The local effective thermal and electron particle diffusivities are inferred and compared with those from similar non-enhanced discharges produced by shallow pellet fuelling. The core diffusivities during the enhanced phase are found to be more than a factor of 2 lower than those in the non-peaked discharges, with improvement localized within the plasma core. Enhancement in global confinement is generally modest but operation at low edge q appears to increase the volume of the enhanced region and the magnitude of global confinement. The enhanced phase is terminated by a magnetohydromagnetic (MHD) mode localized off-axis. Operation at higher central q by earlier injection of the pellet and higher current delays the onset of MHD and extends the duration of the enhanced phase. Operation at low q increases the radial extent of the core region