Transfers are typically performed with an ice pack and at 4°C to mitigate the heat produced. A high field option exists for a single gel, which may bring transfer time down to as little as 30 minutes, but it requires the use of high voltage (up to 200 V) or high current (up to 1.6 A) and a cooling system to dissipate the tremendous heat produced.
During WB, addition of SDS increases the relative current, power, and heating during transfer, and may also affect antigenicity of some proteins. Increasing methanol in the transfer buffer decreases protein transfer from the gel and increases binding of the protein to nitrocellulose membrane.
Consider that electrical resistivity can also be altered by temperature. If not kept at controlled temperatures, there would be gradual increase in resistivity and build-up of heat. This is why some gel apparatus may have constant amps/volts settings. Warm gel also has the risk of breaking apart in your hand. Another side effect of heat could be that transfer could be negatively effected as increased thermal motion as a result of heat buildup would not favor binding to the membrane (purely theoretical).