The tappets are hydraulic and not adjustable, so I was informed when I brought mine in to get her looked at.

The main cause of the tappety noise will be most likely be down to Oil viscosity. When it's cold the oil will be thicker, until it heats up becoming more fluid. Thus the engine having less work to do when the oil is circulating at the correct temperature.

I would go as far as giving the car a good service replacing all the fluids and spark plugs, leads, filters, etc.