I've replaced the battery and the alternator on my 2003 Isuzu Rodeo. But when traveling for several hours with headlights on the battery will go dead and the alternator won't charge till it cools off. Another symptom is that the headlights vary in intensity with the speed of the engine.

Sounds like there's still something wrong with the charging system. Did you verify alternator output?
(Volts/amps) Should charge at about 13.5 - 14.5 volts when engine at medium idle. About 65 amps w/o a/c, about 85 amps with a/c. If you've got the non a/c alt in a vehicle with a/c, amps falling short may cause intermittent charging/problems.

Does engine exhaust leak blow on alternator? Had this symptom before-it can ruin your alternator also.

Battery going dead-either the battery won't HOLD a charge or the alternator is not charging it. One or the other is your problem. Verify alternator output as described earlier, then need to do a LOAD test on the battery with a full charge.

Hope this helps.