I READ with interest the cold starting problem your reader was having with a Mazda MX-5. It took almost two years to fix my 2001 VVTI model, which felt like it was running on three cylinders for a couple of minutes. Over two months we changed the oxygen sensor, the temperature sensor, the coil packs, checked the valve clearances, and flowed the injectors, all to no effect. Eventually we checked and adjusted the valves cold, and this turned out to be the solution. I hope this helps.
ANOTHER possible cause of the problem. One worth checking.