Ford Repair: 98 F150 running hot, pinion seal, heater core

Question
Its is a 98 F150 cyl standard. I got it from my ex brother in law and I knew he didn't take care of it. I just took it to the dealership and had them change the oil and tires. They said I had a pinion seal leak. It also didn't have any fluids when I took it in. It smells bad when I turn on the heater and it doesn't heat very well. Just blows warm. I noticed yesterday when I started it it was running hot about 2 minutes after I started it. I know that either the heating core needs to at least be cleaned but it's not leaking. I checked the water pump and it's not leaking. What do you suggest? also do you think the problems are related? And whatever it is please tell me it's easy to repair. I've already set aside 2 days to take apart the dash to check out the heating core but do you think that'll fix it?

Answer
Hello Adrianna, If it wasn't taken care of very well sorry to hear that. It is possible it has a restriction in the cooling system possibly in the radiator and or heater core, even though there is no leaks it could still have a bad waterpump, acid in the coolant when it gets old and not changed will "eat" the metal fins which will cause lillte flow of coolant. Thanks Tony