There are many measures of a jet engine's 'efficiency' - thermal efficiency just relates to the ability of the engine to extract thermal energy from the fuel and minimise heat losses. This efficiency improves with decreasing ambient temperature. Consequence - fly higher where the air is colder.
Froude efficiency is related to the increase in velocity imparted to the air mass flowing through the engine, this increases with increasing aircraft speed (since the thrust is equal to the rate of change of momentum of the air mass flowing through the engine, and at higher air flow speeds you need less increase in velocity to produce the same change in momentum, since the mass flow is higher). Consequence - flying faster improves efficiency (to the point where compressiblity starts to create a disproportionate rise in drag)
However, at constant IAS (ignoring compressibility at the intake), the mass flow will be the same, since:
air mass flow rate = Intake area x TAS x actual density = Intake area x IAS x sea level density
...therefore air mass flow rate at constant IAS is the same, regardless of actual air density, but drag is also constant at constant IAS (ignoring compressibility, again), so density plays no part.
Although compressibility plays a part, the general trend in improving efficiency is still valid - one could compare engine fuel flow rates at 210KIAS at low and high altitudes, at which speed high Mach no. effects would not really be playing a huge part; high altitude fuel flow rate would still be less than at low altitude, because the engine is more thermally efficient.