1987 Prelude 2.0 Si - strange problem...

Hi: I have 1987 Honda Prelude 2.0 Si (Fuel Injection). It is running great. I am having a unsual problem during start up for the past 3 weeks. I start the car in the morning, it starts without any problem. When I start the car during afternoons or evening, sometimes the car does not start. It cranks and dies immediatly. Then, I have to wait for 2 minutes and then start again, the car starts! If it does not start, I have to wait for another two minutes and then start. Note that I get this problem mostly when the whether is hot. During rainy or cold days, I don't get this problem. When the car has trouble in starting, sometimes I start by holding the accelerator pedal all the way down...and it works sometimes and the car starts...sometimes it doesn't work. Once I start the car, I don't have any problem during driving. Runs smooth. This starting problem is because of some electrical issue? Another thing I noticed is that my horn is not honking...it honks very very low for a second or two. Does this horn and staring have some connection? I took it to mechanic and he is not able to find out the problem. He told me to tune the engine and I did that (change fuel filter, air filter, clean battery, change the connections, change rotor cup, checked radiator coolent level,...). After that, I did not have problem for a week...then, it started again. Then the mechanic changed the ignition coil. But, I still have problem...he is suggesting to change distributor. But, he is not sure whether it will fix the problem. So, I decided not to do that...any of you had similar condition/experience before? Any idea what's going on... Please tell me what could be wrong... man, I love this car, it is very reliable and gas efficient...please help. Thanks a lot. NG