Can thermals or high density altitude improve fuel efficiency?
For flight time and saving fuel, the density is not relevant. Density is relevant to distance covered if you need a set cross country distance rather than a set time. You would only want to set power to maximum endurance which will be very near best glide CAS, while best true airspeed and ground speeds would change with density the best endurance CAS would not.
It may also be advisable to plan relatively shallow descent angles so that the engine stays within a reasonably efficient power range. Climb with power low enough that you can keep it leaned.(after the initial takeoff and climb out, unless maybe you are at an excessively long desert runway)
Thermals could aid the flight time allowing even lower throttle settings but could also harm as they go both up and down, capturing the right current depends on the pilot's glider experience.
Now where I rent, fuel is included in the per hour price and the goal is usually to get a set distance or set of maneuvers in a minimum time. Just the opposite of what you propose.