Temperature gauge go up when I turn right or stop?

2005 Nissan Sentra - 146K miles. Recently I had the water pump replaced. The last few days I have noticed the temperature gauge go up when I turn right or stop, it does not happen every time though, other than that it is fine. I turn on the heat when it goes up and occasionally heat comes out, other times cool air comes out. I have noticed that once I am done driving the reservoir tank is completely full and has some overflow. I touched the tubing from the engine to the radiator and the top one is extremely hot, the bottom one is warm. I have checked the antifreeze levels and they are full. The antifreeze in the reservoir tank is dirty, not dark but looking like there is grim floating around in it. Any thoughts would be great. Thanks.

All of the symptoms you describe point to an air pocket in the cooling system. When the water pump was replaced the cooling system should have been refilled and bled of any air. If this was not done there could be air in the system. Some engines have a special air bleed valve to remove air from places it gets trapped while the cooling system is being refilled.

Thanks, I did not even think that could be the problem, I posted the issue to various places and everyone says it could be the same thing.