The temperature dependence of the electrical characteristics of field-effect transistors (FETs) based on polymer-sorted, large-diameter semiconducting carbon nanotube networks is investigated. The temperature dependences of both the carrier mobility and the source-drain current in the range of 78 K to 293 K indicate thermally activated, but non-Arrhenius, charge transport. The hysteresis in the transfer characteristics of FETs shows a simultaneous reduction with decreasing temperature. The hysteresis appears to stem from screening of charges that are transferred from the carbon nanotubes to traps at the surface of the gate dielectric. The temperature dependence of sheet resistance of the carbon nanotube networks, extracted from FET characteristics at constant carrier concentration, specifies fluctuation-induced tunneling as the mechanism responsible for charge transport, with an activation energy that is dependent on film thickness. Our study indicates inter-tube tunneling to be the bottleneck and implicates the role of the polymer coating in influencing charge transport in polymer-sorted carbon nanotube networks.