What would be most effective way to transfer heat in the following situation?
Specific conditions: A vertical cylinder or pipe, 30-100cm long, 5-10 cm in diameter, heavily thermally insulated except at the bottom, placed in a solid medium (except at the top, which is in air) whose vertical temperature profile varies on an hourly basis and will change polarity (delta T=T_top - T_bot will change sign), and has a temperature difference of around 2-10ºC.
The bottom of the cylinder is attached to a heat "sink" embedded in the solid surrounding medium. The top has a thin insulation layer between it and the air.
The goal is to tie the top temperature as close to the bottom temperature as possible
My first thought was to use a solid metal cylinder (likely aluminum not copper for cost reasons) since conductive heat transport is agnostic to the top/bottom temperature polarity.
It's tempting to use free convection in a pipe using water etc, which is presumably far more effective at driving heat transport. However, if the top is warmer than the bottom, full-cylinder convection won't happen. Forced convection or pumping is out of the question.
What would be the best strategy here? Would a mix of metal conducting rods in a cylinder otherwise full of liquid be even better?
Update: diagram upload as requested.