I'm freezing this winter.!!!
 

I have a Jeep Cherokee Sport and heater comes on, but heat not to capacity blows cold for about a half hour when tryingto warm.

Have you had any work done on it recently or not?

Sounds like a bad thermostat - like it's stuck open all the way so it takes forever to heat up in the cold.

Could be a couple things. Could be the blend door, or the actuator, the heater core, or the thermostat. When was the cooling system serviced, if ever? This includes a flush. Do the heater hoses get warm? Is one noticeably colder than the other? Do you smell coolant in the cabin with the heat on? Do the windows fog up with the heat on when its cold out? Need more info.

Cab heat is a product of engine heat.

First thing I do is to use a laser thermometer and point it directly at the thermostat housing of a hot engine. That is a valuable data point. These thermometers are cheap and everybody that does any work on their vehicle needs one. You might need it to help troubleshoot a heater core as well.

Also as already mentioned, what is the history of routine cooling system maintenance? IE: flush, fill, new thermostat, radiator cap??

One thing that is a classic case for this is a plugged heater core. Have you flushed your cooling system and heater core lately?

Heat blend door actuator
 

I had a similar issue last year, i flushed the heater core, which was a good thing to do but not the solution. The culprit to my problem was with heat blend door actuator was frozen and would not allow heat to pass into the cabin since it was always closed. It was a quick fix located under the glove box.

What are your outside temps? When I was in Montana during one winter I had to block off part of my radiator air flow even though everything was brand new and working correctly just to keep the thermostat open.