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Building upon the compact wavefunction ansatz of the multi-layer multiconfiguration time-dependent Hartree (ML-MCTDH) method, we present a new scheme for simulating finite-temperature quantum dynamics based on purification. Here, a density operator is mapped to a single ML-MCTDH wavefunction in an enlarged Hilbert space, comprising physical and auxiliary degrees of freedom. In the key step, one obtains a pure-state representation of the canonical density operator via imaginary time-propagation of the infinite-temperature state. The most important observation is that this state can be exactly decomposed as a Hartree product of maximally entangled combined modes, each combined mode consisting of a physical degree of freedom and its auxiliary counterpart. Through dynamically pruning the node ranks of the ML-tree during the \u201ccool down\u201d stage yields a compact finite-temperature wavefunction, thus accelerating the real-time propagation and enabling finite-temperature simulations of multidimensional, correlated molecular systems. Our method circumvents both intensive statistical sampling and costly tensor-decomposition of the full density-operator, while being broadly applicable to model Hamiltonians and general ab\u00a0initio potential energy surfaces alike. Two applications of the method are presented: benchmark results on the thermal ground-state of H2O, as well as temperature-dependent infrared absorption spectra of the more challenging, floppy H3O2\u2212 anion.<\/jats:p>","DOI":"10.1063\/5.0355267","type":"journal-article","created":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T14:23:04Z","timestamp":1791901384000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Cooling down trees for finite-temperature quantum dynamics: Purification within ML-MCTDH"],"prefix":"10.1063","volume":"165","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-1687-7186","authenticated-orcid":false,"given":"Niclas","family":"Krupp","sequence":"first","affiliation":[{"name":"Theoretische Chemie, Physikalisch-Chemisches Institut, Universit\u00e4t Heidelberg , INF 229, 69120 Heidelberg,","place":["Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4629-414X","authenticated-orcid":false,"given":"Oriol","family":"Vendrell","sequence":"additional","affiliation":[{"name":"Theoretische Chemie, Physikalisch-Chemisches Institut, Universit\u00e4t Heidelberg , INF 229, 69120 Heidelberg,","place":["Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,10,13]]},"reference":[{"key":"2026101310211788500_c1","doi-asserted-by":"publisher","first-page":"817","DOI":"10.1126\/science.275.5301.817","article-title":"On the quantum nature of the shared proton in hydrogen bonds","volume":"275","year":"1997","journal-title":"Science"},{"key":"2026101310211788500_c2","doi-asserted-by":"publisher","first-page":"5246","DOI":"10.1021\/ja0424676","article-title":"Temperature dependence of quantum effects in liquid water","volume":"127","year":"2005","journal-title":"J.\u00a0Am. 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