Volcanoes with highly-developed and shallow hydrothermal systems may be subject to sudden increases of their surface steam emission at vents in response to either deep forcing (e.g. increase of heat flux coming from the magma chamber) or external forcing (e.g. sudden decrease of atmospheric pressure or variation of meteoric water input). Because the vent plumbing has a limited heat and mass transfer capacity, the rise of steam pressure accompanying the increase of flux may destabilize the system in order to augment its net transfer capacity. This reorganization may, for instance, take the form of an enlargement of existing conduits and vents or to the creation of new ones. In such a case, local and extremely dangerous blast phenomena are likely to occur with devastating consequences several hundreds of meters around. Even volcanoes with a moderate activity and considered safe by the local population are exposed to such abrupt and dangerous events. The detection of early warning signals through temperature monitoring in the vents is of a primary importance and a main difficulty is to correctly interpret temperature jumps in order to reduce false alarms. We analyze time series of the temperature measured in three fumaroles located at the top of La Soufrière volcano in Guadeloupe, which are characterized by their relatively low temperature around 99°C, slightly above the boiling temperature of water at this altitude. Thanks to the long duration of the records from January to August 2017 and to their short 1-s sampling interval, a multiscale analysis can be performed over several orders of magnitude. We show that, despite their complex and sometimes erratic appearance, the temperature variations observed in the vents contain components highly correlated with rain input variations. Some remarkable patterns recurrently appear at different periods and we show that the main temperature variations of more than 10°C are related to the rainfall intensity. Our results illustrate the importance of external forcing on the otherwise complex and possibly chaotic dynamics of the shallow hydrothermal system of La Soufrière. They also reveal that a careful analysis of rainfall forcing must be done to be able to draw any conclusion concerning changes caused by the underlying hydrothermal system.