Raspberry PI periodic connection to the Internet when required

Question

So, I'm looking to use a Raspberry Pi to log into the FON network, but I don't want it to be permanent, only when requested by a NEST central heating controller.

I think 'in the old days' this was the normal process for dial-up systems, but is no longer the case for permanently connected world.

The reason being that only one user (at a time) can use the BT FON account.

Thanx in advance