Gold nanoapertures or nanoantennas can generate strong field gradients enabling efficient optical trapping of nano-objects. Thanks to the accurate nanoscale positioning of plasmonic optical tweezers, trapping single quantum emitters such as NV centers, quantum dots or nanocrystals becomes a trend for single photon sources. However, many factors such as local temperature increase, thermophoretic force or photoblinking all affect this delicate experiment. Here, we use plasmonic nanoantennas to simultaneously trap single colloidal quantum dots and enhance their photoluminescence. The nanoantennas are milled in the gold film and designed to generate an extremely high electric field in the gap. First, we develop a method to measure the local temperature in the trap based on the fluorescence of Alexa fluor dyes under the trapping condition. Second, we demonstrate that the surfactant sodium dodecyl sulfate added in the solution leads to a constructive thermophoretic force in addition to the optical gradient force, which dramatically improves the trap performance. Finally, our dedicated nanoantenna design achieves a high trap stiffness for quantum dot trapping, together with a relatively low trapping power. As the plasmonic nano-optical tweezer automatically locates the quantum emitter at the nanoantenna hotspot without further processing, combining nano-optical tweezers with single emitters is a promising route for quantum technologies and spectroscopy of single nano-objects.