For maximum specific range we require best airframe efficiency and best engine efficiency at the same time.
Fuel flow in propeller aircraft is proportional to power required, so best airframe efficiency means getting the best TAS to Power ratio. This occurs at Vmd.
Fuel flow in jet aircraft is proportional to thrust (which is equal to drag in constant speed level flight). So best airframe efficiency means getting the best ratio of TAS to drag. This occurs Vmrc which is about 1.32 Vmd.
For best engine efficiency we need to get the best ratio between power output and fuel flow in prop aircraft, or between thrust output and fuel flow in jet aircraft. This ratio is called the Specific Fuel Consumption or SFC.
SFC is the cost per hour in Kg of fuel for each unit of thrust or power produced.
Jet SFC = Fuel Flow in kg/hour / Thrust
Prop SFC = Fuel flow in kg/hour / Power.
For maximum range we need minimum SFC.
SFC varies with a number of factors including the temperature of the incoming air. The colder the air, the lower will be the SFC.
So if the air temperature increases, then the SFC increases and this causes the specific range (and the range) to decrease.
If you are studying for the JAR ATPl Perf exam then the answer you require is that SFC is directly proportional to air temperature.