Repair prices are tough to judge because various areas are higher or lower cost of living.
We he asking for $149 for the entire repair, or just the labor, plus extra for the part? $149 would be fine (here in Northern Illinois) for the entire repair, but a touch high for just the labor.
Sounds very high indeed. To give you an example, I live in an area that the median income is $150,000 a year and houses cost (on average) about $350,000 (I live in a dinky townhouse). Anyway, in our area, the average for trip and labor to do that job would range from $80 to $100, again for trip and labor combined.
You could ask him what his labor rate and structure is, then time the repair. That part should take no more than 20 minutes for an experienced repairman, probably less.
The part called “control box” is just a box and nothing else.
The cold control (aka thermostat) is located in this control box together with a few more parts.
In my opinion the problem with your fridge has nothing to do with the cold control.
It is very possible no parts has to be replaced at this time at all.
One of most common cause for the vents (on top, between the freezer and the fresh food compartment) to be blocked by ice formation is warm air. It could happen if the doors been open too often and/or for long time.
You have to remove the air diffuser and vent cover and clean everything from icicles and/or snow.
Considering this has been a repeated problem, you may have a bad door gasket allowing warm room air to enter the refrigerator. Look for any areas that the gasket is not closing all the way.