After doing some research, I managed to find a good climate details of Kota Kinabalu:
Kota Kinabalu Precipitation
Mornings are usually clear at any season. Sabah lies below the typhoon (hurricane) belt, though the tail-ends can cause strong winds and rain during the typhoon season.
At Kinabalu Park Headquarters (1,560m a.s.l) the mean monthly temperature is approximately 20 ºC, with a daily fluctuations of 7 – 9 ºC. Mean annual rainfall at this location is 2,380mm.
A common climatic feature to the park are bright early mornings, followed quickly by clouding mid-morning, which obscures the mountains by mid-day. Showers usually occur on the upper slopes in the afternoon.
Although they say ‘the driest time’, a good raincoat is a must. Otherwise, you may get wet when it rains while on the way up to Laban Rata, at the slopes of Kinabalu.