There are several questions to ask:
How critical is 35.2 to 39.4? What happens if it is 39.8? Or 42?
If nothing happens, why is the spec. so tight and why are you bothering to calibrate the gage. If it may create bad material, slow down the process, etc - it is probably best to have it calibrated. If the building explodes, it should definately be calibrated. You need to make the call based on the risk and cost/benefit analysis.
What type of device is being used? RTD, Thermocouple, thermometer, etc?
For a range that narrow you may need to look at calibrating both the sensor (RTD/TC) and the readout device. Its been awhile, but I recall you can get a TC certified - for big $$$. They are not very accurate devices. Even if you have resolution to .1 degree, you need to make sure the device is still accurate enough.
Hope this helps,