Put simply, the weather is perfect for cycling all-year-round. However, Tenerife has many different "micro climates", depending on the location on the island. For example, there are places that are always windy; other places are prone to fog; some places receive less rain; while other places can be quite hot. It is better to give a range of expected temperatures. Along the North coast, the temperatures are approximately 15°C in Winter, 24°C in Summer.

Tenerife Weather Forecast:

These two weather forecasts are the most reliable:
Firstly, the BBC 5-day weather forecast for Tenerife South Airport, data from the El Medano weather station.
Secondly, the Spanish Medioambiente site 7 Day Weather forecast for Puerto de la Cruz.

Cycling in the winter:

During winter, you can expect to encounter ice above 2000m for a few days of the year. When that happens, access to these roads is restricted or cut completely, but the roads are usually cleared of ice promptly.

It is usually cold at such altitude (leg warmers and a jacket are needed for the descent from Teide). The good news is that at such high altitudes, the roads are located well above the cloud layer (1000 - 1500m)... so you can enjoy blue skies and sunny weather all throughout the year up there!

The "Calima":

Several days a year, Tenerife and the neighbouring Canary Islands are engulfed in a phenomenon known as the calima. This is essentially a suspension of dust which remains in the air because it is so fine. It initially blows over from the Sahara desert, raises temperatures considerably, and usually dissipates within a day or two. During a calima, there is a localised temperature inversion, meaning the higher you go up, the hotter it gets. It's not uncommon for Las Cañadas to experience temperatures approaching 40°C, so don't forget your suncream. When the visibility is greater than 2km, it is then called a "bruma". These are not the same as a sirocco. Cycling during this time can't be good for your lungs, but that doesn't seem to stop the locals going riding anyway!

Current Live Atlantic Satellite Map:
(click to enlarge)