Because the BHP of an engine varies with intake ambient air temperature and pressure, the rated BHP of an engine is measured at sea level air pressure of 29.92" Hg and air temperature of 59 deg F or 15 deg C. If these parameters are not available, then the obtained BHP is corrected to account for any variation making possible accurate comparisons among engines, regardless of the measurement environment. Considering only the relationship of intake air temperature to HP, the power varies essentially as the square root of the change in ABSOLUTE temperature.

For references consult:
High Speed Combustion Engines by P. M. Heldt, 16th edition, p.638

The Design and Tuning of Competition Engines by Philip H. Smith, 5th edition, p.370-71.

Assuming the Protege 2 liter engine develops 130 HP at 59 deg F which = 15 deg C, this represents 288.15 deg K on the Celsius absolute temperature scale. To calculate change in HP, take the square root of the quotient of the standard temperature (288.15 deg K) divided by the proposed temperature in deg K and multiply that by
130.

For example:
What is the HP output at 30 deg F (-1.11deg C) where the absolute temperature is 272.04 deg K?
1. Divide 288.15 by 272.04= 1.059
2. Take the square root of 1.059=1.029
3. Multiply 130(1.029)=133.8 HP

What is the HP output at 0 deg F (-17.78 deg C) where the absolute temperature is 255.37 deg K?
1. Divide 288.15 by 255.37=1.128
2.Square root of 1.128=1.062
3. 130(1.062)=138.1 HP

Conversely, one can calculate the HP decrease as ambient temperatures rises above the standard.

The temperature at 80 deg F (26.67 deg C) where the absolute temperature is 299.82 deg K.
1. Divide 288.15 by 299.82=.961
2. Square root of .961=.980
3. 130(.980)=127.4 HP

In the same manner some other representative temperatures are:
100 deg F=37.78 deg C=310.93 deg K=125.1 HP
140 deg F=60 deg C=333.15 deg K=120.9 HP

To calculate HP at any given temperature, simply convert the ambient temperature either F or C to absolute. For those of you who want to work exclusively with the F scale, you can use the Fahrenheit absolute temperature scale where 59 deg F=518.67 Rankine.

To convert temperatures from one scale to another see this website: www.onlineconversion.com

Clearly the results indicate we should attempt to provide ambient temperature air, as opposed to underhood air, to the intake for maximum performance.