During that elevated temperature period, the lake reached temperatures of around 38C, and scientists expected the lake to then cool as it had done many times before.
While that happened over the past two months - when the lake had cooled to around 20C - the water began warming again last week, rising at a rate of around 1C each day.
"Following previous heating cycles, we expect the lake to continue heating for the coming weeks," Kilgour said.
"Coincident with the increasing lake temperature, we have also noticed that the level of volcanic tremor has increased."
This was a characteristic feature of a heating cycle and represented the increased flow of hydrothermal fluids into the lake.
Previous heating cycles had shown this increased tremor to last for days to weeks.
"As part of our normal routine monitoring, we aim to visit Te Wai ā-moe this week to collect water and gas samples from the lake," he said.
"The Crater Lake has undergone many heating and cooling cycles in the past and we don't see any unusual signs of increased unrest."
The Aviation Colour Code for Mt Ruapehu also remained at Green, the normal level.
"While this is the case, it is a useful reminder that eruptions can occur with little or no warning."
The last time Ruapehu erupted was on September 25, 2007, causing a seven-minute-long earthquake, two lahars and flying rocks - one which crushed the leg of primary school teacher William Pike when it landed on Dome Shelter near the crater.