Etymology
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thatch (n.)
Old English þæc "roof, thatch, cover of a building," from Proto-Germanic *thakam (source also of Old Norse þak, Old Frisian thek, Swedish tak, Danish tag, Middle Dutch, Dutch dak "roof," Old High German dah "covering, cover," German Dach "roof"), from PIE root *(s)teg- "to cover."
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*agh- 
Proto-Indo-European root meaning "a day" (as a unit of time). The initial d- in Germanic is of obscure origin.

It forms all or part of: adays; Bundestag; daily; daisy; dawn; day; holiday; Reichstag; today.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit dah "to burn," Lithuanian dagas "hot season," Old Prussian dagis "summer."
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