My Mazda 3 2006 works often fine during cold start. During some warm days and when I drive longer distances I got some starting issues. In some cases when I tried again after 20-30 min. It worked fine again. I have even installed a new battery but It could not solve the problem.

 

How many miles/km's has it done?

Could be a dying starter motor. Doesn't like the extra resistance when hot.

 

Not that much aroumd 1200

 

Have you tried a new starter?