1994 honda accord lx won't start on hot day?

I'm in Arizona where it about 110 every day so my car will start in the morning but rarely if in the afternoon. Ijust replaced my fuel filter and my battery cables however my battery is pretty old. Could that be the problem?

Top suspect is the fuel pump relay, also called the "main relay." The solder connections break from vibration and they tend to be heat sensitive that way. See the source for details and a test to use when it is not starting. The relay in your car is mounted under the dash above the steering column, on a long stud sticking down from the very top of the dash. For that reason, it may start if you give the top of the dash in front of you a whap with your hand when it doesn't start. At least whapping it will make you feel better.

Usually when heat gets to the battery it goes downhill very rapidly - a week or two from the first trouble to not working ten minutes after you shut it down. (I lived in Phoenix for 25 years and never got a battery to last more than two summers.)

Very possible, go to a local auto store and have your battery checked for free, they should also be able to check your starter and alternator which could be causing the issue.