2002 jeep liberty has very little or no heat also overheats in warm weather changed water pump and thermostat also had system flushed

There is something called a blend door in the heater box. This door is what moves to change from cold air to warm air. The part is 86 dollars online. http://www.factorychryslerparts.com/products/JEEP/LIBERTY/ACTUATOR-Blend-Door-AC-and-Heater/4341513/05066519AA.html

Could I ask why you changed the waterpump in the first place?

Sounds like low flow issue. Flush and clean system, PROPERLY! Buy a flush kit, drain system, blow compressed air through, fill with cleaner/water mix, run for 30 min with heat on, drain system, blow out with compressed air, fill with water, run for 30 min, drain, blow out with compressed air, fill with 60% coolant mix.

so what was it.
bad mech. service (sure was)
or bad head gasket
or bad water pump.>

While it doesn't seem likely, if you've changed, or had the thermostat changed.... I'd say you got a faulty thermostat. I am curious as to what your temperature gauge says the temperature of the engine and coolant is.. If your gauge is showing hot, I can think of two more possibilities... the water pump isn't pumping right... and, if the water pump isn't working right, the problem can be a cracked head or block, which can cause an airlock in the coolant system. Check the coolant or radiator cap.

Could be your blend door is not opening all the way on heat,here's a link to look at.

Sounds like the coolant system needs flushed out with a good flush.

most likely the water pump.

Does it look like coolant leaking? Same color? If so, it could be. That or the water pump. Go for the thermostat first. They are more common to go out. It would explain the lost in heat.

do you have a "check engine" light on? A bad temp sensor would give a wrong reading. Do you get heat from your heater core? Also make sure you are getting a good flow from catalytic converter and muffler so you know they aren't plugged heating up engine temp. Also make sure all your heat shields are in tact. Are you using 50/50 mix or mostly water? Though in cold temps you normally want to use more antifreeze less water, I would try more water, less antifrezze.