Korrupted

I have a question about my buddies jeep! He has a 93 Jeep Cherokee, auto. 6 cyl. 4.0 H.O. and 150,000 miles. He is having trouble with starting it up. The first time he starts it, the jeep starts right up. If he turns it off while the engine is still cold he can't re-start it. It takes about 15 mins. before it will start again. But if he drives for a while and turns it off and re-starts it while it's hot it starts right up. He has a new starter and he had the battery, alternator and charging system checked and it was all good! He thinks it may be the battery terminal cables. They cost about $100 and his time. Any advice would be appreciated!!!