Toyota Repair: 93 Paseo Overheating, control cables, seperate issue

Question
I have a problem with overheating after driving for about 5 - 10 minutes.  The engine was replaced by a local high school with a Japanese motor.  It ran fine for about 2 weeks then it overheated.  I found a hose came off between the firewall and the engine.  Once I put it back on and put coolant back into the radiator it continued to have problems with overheating.  I replaced the t-stat and radiator - still no change.  Possibly related - about 6 months ago I took my dash apart (w/o disconnecting the battery) to get to an odor problem but when I put it back together the heater would not blow warm air and the A/C would not blow cold air.  Both would only blow luke warm to cool air and the blower switch now only operated on high speed (acts as if both the heater and A/c are operating at the same time.

Answer
The heater and a/c problem are a seperate issue, it sounds like it may be a control problem, one of the control cables is not adjusted correctly or is disconnected, make sure the control cable at the heater valve is adjusted so the valve shuts off completely with the control knob in the "cool" position.
There is a resistor under the dash in the air duct near the blower motor that controls the fan speeds, a common problem is that the resistor burns out and you will get only one fan speed.
None of these have anything to do with the overheating problem.
Does the engine start to overheat quickly or does it take a while, does it overheat driving on the highway at sustained speeds or only in stop and go conditions or only at idle?
Be sure the cooling fan on the radiator comes on.