Range rover 84 3.5 hard to start when warm not all the time though

sounds to me like the cat converter is stopped up. Usually the engine will die out after a short while though if it is clogged. Over time the pressure will release enough for the engine to start again. The coil could be getting hot and fails to spark, but again this should kill the engine after a short while. If you let the engine idle will it die on its own? more info if you can supply any would be great.

check for faulty hydraulic lifter/s Check for correct viscosity of oil. Check for correct type of oil filter ( must have an anti-drain back valve in the filter.)

Sounds like bad starter, solenoid contacts worn out

When operating properly the HSE temp guage should be straight up on your guage or halfway between cold and red. If your fluid level is correct and its not getting near the red zone you may have some radiator blockage or trapped air (especially if your system fluid has been recently serviced or drained and replaced). In any event, the red zone on your dash guage should be avoided at all costs. Overheating of this engine can and most likely will be disasterous. Best advice, don't take chances here, pay for a couple hours shop time at your best Rover shop and have it diagnosed correctly the first time. Do not take it to any shop or mechanic that does not work on Rovers regularly. There are many aspects both operational and mechanical that are unique to the Range Rover cooling system. Hope this helps, good luck.

Very likely the fuel pump has failed, if you mean you tapped on the gas tank
and it finally started. When a pump fails, sometimes rapping on the tank will re-energize it briefly or maybe even a couple of times before it gives out for good.
If you were tapping on the gas pedal, though, and it just started, your mechanic will have to look at it. Too many electrical fault possibilities, Scott, it needs proper diagnosis to find the p[roblem.

I have experienced many electical demons with all my British cars. The nav units can and do fail. I had a goofy one this summer and the only way it got fixed was to replace it. The module not the head unit

Cause for this should be looked at and assesed imediatly for safety reasons. This could be a loose wheel, bad tie rod end, ball joint or something steering related. All causes can lead to a very bad situation for you. Please take it and have it looked at for your safety.

Its the cold start sensor, happened to me a few years ago. Sensor located just behind thermostat housing, there are two and you will see the wiring plugs going to them. I am sure it is the front one. Cheap repair, lucas part is about £6.
Be careful though, steel into alloy! ease it out gently and take time putting it back in to avoid cross-thread. Fiddly job but not hard.

Check the fuel pressure when the vehicle is cold and compare it with when it's hot.Also check the fuel return dump valve , that this isn't returning too much fuel.

The normal reason why a hot engine doesn't start is the choke. Your fancy new range rover will have a computer controlled choke that will be activiated by a temperature sensor. maybe in his enthusiasm to replace expensive parts your dealer missed replaciijng this cheap little component. i don't see it in the list of replacements in your posting. Another possibility is that the sensor is OK but just disconnected.

In my ancient range rover I have a manual choke but essentially the same engine. I know that if the motor is hot I can't start it with the choke on.