No. I doubt anything less than a decade would make much of a difference.
It's taken a century or so to raise the temperature in the tunnels by around ten degrees C. That already includes the cooling effect of cold air being pushed into the tunnels for most of the year, balanced by the relatively small number of days a year when the air temp in London is more than 14C.
Without that cooling heat has nowhere much to go. It will radiate out into the air, which will make its way up and out rather slowly. And it will diffuse into the clay/soil around the tunnels, even more slowly.
A fully passive cooling-off period would take years - at least.
The problem isn't impossible to solve. All kinds of active cooling solutions are possible.
The problem is that it's impossible to solve affordably. You effectively have to build a heat exchanger the size of central London, which is never going to be cheap.
