If you want to be faithful to the original derivation of degree-days, the equation would be to calculate the daily mean as the average of the max and min temperature of the day, and then subtract that from the base temperature (65F in the US that then got translated to 18.3 C elsewhere), and then sum the positive values over all the days.

Some tidbits on how this "classical" formulation evolved:

1. It was used to estimate the amount of coal needed in Chicago (?) in the 1930s.

2. Max and min temperatures were used because hourly temperatures were unavailable.

3. 65 F can be interpreted as the balance point temperature (BPT) of a building, below which heating would be required. As buildings have gotten tighter, there was talk 20+ years ago that lower BPTs should be used, but that became irrelevant with the proliferation of simulations, leaving 65 F degree-days as just a general climate index.

4. Using hourly values, i.e., degree hours/24, will give slightly higher values (3-8%), but these paradoxically often correlate not as well to building energy use, because they ignore building thermal inertia.

Update:

In answer to the previous question, I've never bothered to check if the equation has been defined in some standard, although it has been described in a lot of technical literature (just do a Google search). Frankly, I don't understand the compulsion for seeing methods standardized.

While I'm on this subject of building energy-related climate indicators, I'd like to repeat that degree days is just the earliest indicator developed and only addresses sensible heat loss/gain, i.e., temperature. There have been similar indicators proposed for humidity (Latent Enthalpy Days), solar (Heating/Cooling Insolation Days), even infiltration (Infiltration DD's), but they've not been widely used or adopted. For a description of these indicators, please look at this old paper that I wrote 28 years ago (if nothing else, it might impress you with its age!)

Another note for the curious: I recalled that the equation in the original question had two differing temperatures. This actually works well for getting cooling degree days/hours to correlate to building loads. The logic is that the two temperatures correspond to the building's BPT with and without ventilation, i.e., windows open or closed. There's even a term for it, "Vented Cooling Degree Hours" (invented by someone else), but described in my 1982 paper. Alas, it never caught on with the building energy community, and a colleague at UC Berkeley likened it to "tuning up a 1950's Thunderbird", i.e., refining an obsolete technology.

To answer your equation about the equation, your equation is correct except the standard definition uses the same number for the base and threshold i.e. you would do HDD12 or HDD20 not HDD20/12. You sum up the difference in temperature between the base and the actual when the actual is above or below the base. You also need to use the average daily temperature. Most calculators will actually do the sum on an hourly basis and then divide by 24 to get the daily numbers.

An important question to ask is what base do you want to use? Here in the US where we do it in Fahrenheight, typical numbers for building scientists are HDD50/CDD50 and HDD65/CDD65. You can find lots of data at http://www.degreedays.net/

Your question about metric is not clear enough. What is the paper about and what are you trying to describe about the climate? Are you trying to just compare the required heating and cooling potential? Then HDD and CDD are fairly decent and well accepted.

If you want to succinctly discuss the effect on building design and overall energy including things like humidity, then I think talking about the ASHRAE climate zones is better (i.e. things like 2A, 4C, 7B, etc). These are more comprehensive, but coarse, distinctions. But, then you need to reference a paper that describes how these were determined rather than give an equation.

If you have a discussion of renewable energy in the paper, then neither describes the solar or wind potential at all and you would want another measure like average solar energy potential Wh/m²/day.