Map from Google - Krabi

The climate of Krabi is tropical, hot all year round, with a rainy season, due to the southwest monsoon, which runs from May to October, and a dry season from December to March. In March and especially in April, before the monsoon, there is a certain rise in showers, while in November there can still be abundant rainfall, especially in the first part, either for any delay in the retreat of the monsoon, or for the passage of a tropical cyclone (see below). In the dry season, however, there can be some showers as well, especially in December, when occasionally some of them may be particularly intense.
The town of Krabi, the capital of the province of the same name, is home to an airport, and more than a tourist attraction in itself it is the starting point to beaches, islands and natural parks, such as the beaches of Ao Nang, Phra Nang, Noppharat Thara, Railay, Tonsai, Klong Muang, and the islands of Koh Siboya, Koh Jum, Koh Lanta, Koh Hong, Koh Yao Yai, Koh Yao No, the Phi Phi islands, the Four islands, and parks such as the Ao Phang Nga National Park and the Than Bok Khorani National Park.

Krabi Province, map

The temperature is high throughout the year, so that on average highs never drop below 30 °C (86 °F). However, from December to March the humidity is slightly lower. At night, temperatures rarely drop below 20 °C (68 °F), although this can sometimes happen between December and March. From February to April, before the arrival of the monsoon, there is a slight rise in temperature, in fact this is typically the hottest time of the year (together with May, the first monsoonal month), so much so that it often reaches 35/36 °C (95/97 °F). It goes a bit better in the islands and along the beaches, also because of the sea breeze.
Here are the average temperatures.
Average temperatures - Krabi
KrabiJanFebMarAprMayJunJulAugSepOctNovDec
KrabiJFMAMJJASOND
Min (°C)222223242423232323222322
Max (°C)333434343332323131313131
Min (°F)727273757573737373727372
Max (°F)919393939190908888888888

Rainfall amounts to 2,000 millimetres (79 inches) per year; in this coast overlooking the Andaman Sea, the rains during the period of the southwest monsoon are more abundant than in the other coast of peninsular Thailand, that of the Gulf of Siam, because the south-western winds hit it directly.
Here is the average precipitation.
Average precipitation - Krabi
KrabiJanFebMarAprMayJunJulAugSepOctNovDecYear
KrabiJFMAMJJASONDY
Prec. (mm)3045100145170195200265275325180702000
Prec. (in)1.21.83.95.76.77.77.910.410.812.87.12.878.7
Days559121616181819221810166

The amount of sunshine in Krabi is good in the driest period, from late December to March, while during the rainy season the sun alternates with cloudiness, which can be more or less durable, and can give rise to rain showers.
Sunshine - Krabi
KrabiJanFebMarAprMayJunJulAugSepOctNovDec
KrabiJFMAMJJASOND
Sun (hours)686655555456

Sometimes, Krabi like the rest of Thailand can be affected by tropical cyclones. This area on the Andaman Sea is relatively protected, since cyclones can be formed nearby, but then they will head towards the Bay of Bengal, and this happens preferably between April and December, with two peaks at the beginning and at the end of the period (April-June and October-December), while typhoons can arrive from the east, but generally pass more to the north, from the South China Sea to mainland Thailand; however, from time to time they can also move to these latitudes, and this has happened in the last decades from mid-October to about 20 December.

Phra Nang Beach

For swimming, the sea in Krabi and in the surrounding areas is warm all year round. It should be said that during the summer monsoon period the sea can be rough, and there can be dangerous currents.
Here is the average sea temperature.
Sea temperature - Krabi
KrabiJanFebMarAprMayJunJulAugSepOctNovDec
KrabiJFMAMJJASOND
Sea (°C)282829303030292929292928
Sea (°F)828284868686848484848482

When to go

The best period to go to Krabi for a beach holiday is from late December to March, being the dry season. In March and April it is hot and the pre-monsoon rains become more frequent, so the absolute best time is from December to February.