95 Chevy 1500 (4x2)

This is what i've noticed. When i cut the heat on, the hose running from the core to the water pump loses heat meaning before i cut it on, it's so hot that i can't hold it. When i cut it on, it becomes warm to the point where i can put my hand around it constantly. Is this suppose to happen? Another thing i've noticed is that the tank on the right side of the radiator(facing vehicle) is extremely hot and the tank on the left side is not? Is that suppose to happen? Remeber, i don't know much about HVAC so i'm learning as i go.

P.S.
Heater Core, thermostat, water pump have been replaced.

Well i discovered that the intake hose had a very very slight seapage at the nipple. Ironically it wasn't seaping enough to leak on the ground. What i did was replaced the hose and the nipple and by golley, the hose running to the water pump is hot to the touch. I can't hold it. I think i may have fixed the problem. Oh, also when i disconnected the old nipple, a piece of black gasket sealant was sticking out the hole. I think it was blocking some of the flow. I'll give it a couple of days and see what transpire.

This is what i've noticed. When i cut the heat on, the hose running from the core to the water pump loses heat meaning before i cut it on, it's so hot that i can't hold it. When i cut it on, it becomes warm to the point where i can put my hand around it constantly. Is this suppose to happen? Another thing i've noticed is that the tank on the right side of the radiator(facing vehicle) is extremely hot and the tank on the left side is not? Is that suppose to happen? Remeber, i don't know much about HVAC so i'm learning as i go.

P.S.
Heater Core, thermostat, water pump have been replaced.
This is all normal stuff. Hot water from engine enters radiator on driver's side, which is why it is hot there. The coolant/water flows across teh radiator to the passenger side, dissipating heat during this voyage. That is why the coolant tank on the Pass side is cooler.
Same thing for your hose from heater core to water pump. When heater is "on", with fan blowing, the heater core is acting like a miniature radiator, (heat exchanger), and it cools the water that flows through that hose, by transferring the heat to the air passing through the core. When heater is off, water is still flowing the same path, but does not get cooled by the heater core, so it stays hot.