Dear,

Climatic changes can effect the biogas production. Generally, the rate of fermentation is increases on increasing in temperature. hence, if temperature increases then the rate of bigas production will also increases or vice-versa.

Methane is produced anaerobically by certain Archaea.  Since warming often increases rates of aerobic respiration, there will be oxygen deficits in aquatic environments, thereby increasing rates of methanogenesis.  Also, some methanogens use the organic acids produced by fermentation as their electron donors, so there is a strong coupling there.

Do you mean in anaerobic digestion facilities? The digestion in those facilities is a mesophilic (37°C) or thermophilic (50°C) process. The higher the temperature, the faster the process will be. However, thermophilic digestion is more instable than mesophilic digestion. To keep the digesters at those high temperatures, the digesters must be heated.

Climate change, as in higher temperatures, will not have a large effect on the methane production, since it almost wont result in a higher temperature inside the digesters.