I saw new hose on roverparts that leads me to believe mine is connected backwards...
Should mine cross?

 

you are correct, the hoses are connected to the opposite inlet, outlet pipes. It doesn't really matter, the heater core won't know the difference. Some shops actually swap the hoses in an effort to get the air out of the cooling system. If you aren't having cooling issues and you don't have air in the system, I won't touch it. Phil

 

It does make a huge difference when you consider the 2 functions of the heater core, one being heat the other being special routing of the water from and to the engine via the t/stat.
Whats with those old warn out grey factory plug wires, get rid of them along with some good plugs and your truck will run better.

 

Mike, isn't the heater core just a small radiator with an inlet and outlet tube. You will have constant flow through the heater core. When you turn on the heater, The heater fan blows air across the heater core and into the passenger cabin. By swapping the inlet from the outlet, you wouldn't change the flow coming in from the engine, you would just change whether the hot coolant would be directed into the bottom or the top of the heater core and the cooled coolant would then come out of the other. You wouldn't change the flow in or out of the engine and the thermostat. Am I missing something? Other than what is mentioned, would there be any other impact by connecting the hoses in the opposite pattern. Thanks, Phil

 

I now have HEAT !!! Thanks MIKE!!!
I replaced a leaking TB hose last month, and had no overheating, no other weak point or leak, but still no heat.
The reversal of the in/out hoses was the final solution to my heat.

Now I can move on to Plugs and Wires...