Pyrolysis is an energy positive reaction. It requires an initial heat input, but after getting started it produces more heat than it needs. That heat can be used to generate electricity or warm water.
Capturing the heat from pyrolysis in this way does however convert the pyrolysis vapor from hydrocarbon into combustion byproducts, namely C02. This company claims to be condensing all of these hydrocarbons, not combusting them.
For a nice and understandable example of pure pyrolysis without combustion, there is this project [0] wherein an airtight vessel is loaded with biomass, heat/energy is applied with electrical resistive heating elements. The pyrolysis occurs and the resulting vapors are captured and stored as a low pressure vapor for later use in cooking or powering internal combustion engine.
-- How much mirror area [heat] would be needed?
-- Mirror geometry: Troughs may lend themselves to continuous processing and gas recovery a bit better than central point concentrators but they provide less heat potential.
-- Can the economics work if you only process when the sun shines?
In that case, you are totally correct, they'll need an input heat source.