There is a description in 'Sekiso Orai' (Basic encyclopedia) written by Kanera (aka. Kaneyoshi) ICHIJO during the Muromachi period, 'Somen is steamed hot, while Kirimugi is washed in coldwater,' which strongly supports the theory that Kirimugi is the predecessor of Udon noodles.
室町時代には一条兼良の著書「尺素往来」に、「索麺は熱蒸し、截麦は冷濯い」という記述があり、截麦（切麦）がうどんの前身と考える説が最も有力とされる。