I am reading from a thermocouple with the MAX31855 chip using double variable type for greater precision.
Ummm, doubles on Arduinos (except for the Due) are actually 32-bits, which gives you 24 bits of precision in the mantissa for numbers in the normal range of precision. I would imagine giving the posting by pylon that says the MAX31855 only has 14 bits of integer precision means even a float may give you more precision than the device returns (though if you are doing extensive calculations on the value, you may want some extra bits to prevent unintended round-off).
Another thing to consider is floating point is done entirely in software in the Arduinos (both the AVR based ones and the Due). If you are running into performance bottlenecks, you probably should consider using int/long variables instead of double.