I have a Frigidaire freezer FPUH19D7LF1 and came home yesterday and panel showing HI TEMP. Wife was home all day and said there was no alarm. No other indicators on the panel. I can hear the fan running. Tried resetting the breaker and left it overnight. Checked this morning and it was down to 5 degrees which is what it's set to, but then I opened the freezer about 10 minutes later and the HI TEMP light was on again. No alarm sounded. It seems like it's cooling but not very efficiently. I don't know much about appliance repair but I tried looking around some forums and they suggest looking in the back to see if anything is frosted over. I will take a look when I get off work today, but in the mean time does anyone have an idea based on what I posted? Thank you.

Quick guess is the thermistor above the evaporator behind that evap cover inside is erratic or otherwise reporting incorrect temps. It's the little black thing attached to rear wall with red and black wires, and is responsible to for reporting temps to the control board.

Those evaporator coils should have a good, relatively even, layer of frost on them, unless it has just come out of defrost in which case frost should quickly begin to grow on them as they cool. If the frost pattern is not complete, or not at all snap a pic of it and post if possible.

I do see the condenser fan thermostat on the wiring diagram but it is not in any parts listing that I can find. You can bypass it without any harm; it just means that that fan will run anytime the compressor is running. Unless the ambient temperature is very high (100 F or more) the unit should still cool even without a condenser fan running; it just would be inefficient. That thermostat just keeps the noise level down by opening the fan circuit when the ambient temperature is low.

When you say the copper tubing coming from the compressor is cold do you mean the ones coming directly off of the compressor itself? One of those should not be cold if the compressor has been running more than a minute or two. The compressor output line should be pretty darn warm if the compressor has refrigerant to compress.
Most compressors will have the suction line coming from the interior on the left and the output to the high pressure side on the right. High pressure = high temp. There will also be a stub that doesn't go anywhere that is used to fill the machine.

Could be either, if the compressor is running normally and it has refrigerant the refrigerant (R-134a) enters the evaporator (inside of freezer) as a liquid through the capillary tube. It is the tiny tube that looks more like a wire. When the cap tube meets the larger diameter tubes of the evap the refrigerant changes to gas state, this rapid expansion is where all the cold comes from; in simple terms.
If it is very low on R-134a it cannot fill the evap and not much happens. Similarly if there is a restriction somewhere not allowing much R-134a to pass you will also get poor or no cooling. Inefficient compressors are not common but that could be also.
So if you are seeing very little frost on the evap after the compressor is running for 10 minutes you likely have a sealed system issue and unless you have a longer term warranty on the sealed system parts it is probably not cost effective to fix. The company I work for charges $299 for most sealed system labor, add parts and you can easily be over $600.

If none of the tubes on the compressor are hot when it is running there is no compressing happening, that's another indication of a sealed system issue. When the gas is recompressed it creates heat, lack of heat is bad.

TO diagnose farther I'd need to put a tap on the low pressure side and see what pressure that is at, that reading may lead me to inject a dye and refill with refrigerant or tell you to go shopping.