Some solar controllers have a predictive function, i believe the Worcester Bosch boiler/cyl/solar controller can do this, for instance.
Even so I doubt that it can predict what the weather is going to be later on any day!
There are cheap ( £4 ) digital thermometers designed for fitting indoors with the sensor on a 2m lead to be placed outside.
One of those could have the sensor cable extended to achieve what you are looking for.
Tony