the starter relay is a solid-state type in most modern cars these days and have a tendency of deteriorating after some number of years in use especially in a very frequent engine starting and cutting-off. As u hv mentioned tat it occurs only during hot engine start, it could possibly be the unit itself having loose contacts in it and this will leave you with a "tuck tuck" sound but without the ability to crank the engine at all. However, once the engine is much colder, it will be abled to close back the contact and allow u to have the engine to crank again. However, since u could crank the engine but could not get it to ignite, it could be the setting out ur fuel/air mixture being too lean. Perhaps, u could look into it as well.