We present measurements of the equatorial topside ionosphere above Jicamarca made during extremely low solar flux conditions during the deep solar minimum of 2019-2020. Measurements were made in October, 2019, February, 2020, and September, 2020. The main features observed are a large and extended decrease in noontime temperatures unlike that seen in studies at moderate solar flux levels, predawn ionospheric heating as early as 0300 LT, large day-to-day variability in the O+/H+ transition height, and negligible helium ion concentration at all altitudes. Data from the Ion Velocity Meter (IVM) instrument onboard the Ionospheric Connection Explorer (ICON) and the Topside Ionospheric Plasma Monitor (SSIES) onboard the Defense Meteorological Satellite Program (DMSP) satellites are used to assess agreement with ISR data and assist with the analysis of the predawn heating phenomena. We also analyze the data in light of the SAMI2-PE model which shows less agreement with the data than at higher solar flux. The main areas of discrepancy with the data are outlined, such as the absence of significant predawn heating, less pronounced decreases in noontime temperatures, and much higher O+ fractions at high altitudes, particularly in September. Finally, a sensitivity analysis of the model to various forcing agents such as neutral winds, plasma drifts, solar flux, and heat flow is performed. A discussion is presented on bridging the discrepancies in future model runs. Novel techniques of clutter removal and noise power bias correction are introduced and described in the appendices.