Ontology-mediated query answering is a popular paradigm for enriching answers to user queries with background knowledge. For querying the absence of information, however, there exist only few ontology-based approaches. Moreover, these proposals conflate the closed-domain and closedworld assumption, and therefore are not suited to deal with the anonymous objects that are common in ontological reasoning. Many real-world applications, like processing electronic health records (EHRs), also contain a temporal dimension, and require efficient reasoning algorithms. Moreover, since medical data is not recorded on a regular basis, reasoners must deal with sparse data with potentially large temporal gaps.Our contribution consists of two main parts: In the first part we introduce a new closed-world semantics for answering conjunctive queries with negation over ontologies formulated in the description logic ELH , which is based on the minimal canonical model. We propose a rewriting strategy for dealing with negated query atoms, which shows that query answering is possible in polynomial time in data complexity. In the second part, we extend this minimal-world semantics for answering metric temporal conjunctive queries with negation over the lightweight temporal logic T ELH c ,lhs,− and obtain similar rewritability and complexity results. This paper is under consideration in Theory and Practice of Logic Programming (TPLP).