Springbrook NP is a great place to run trails when it's hot, there is water everywhere and most of the trails stay in shady rainforest. The Warrie Circuit is a fairly easy 17km loop with a perfect swimming hole at the half way point. There are plenty of other short trails as well.
Lamington Spiny Crayfish often come out on the trails after rain.
Rainbow Falls is a nice spot for a shower.