Property graphs are a common form of linked data, with path queries used to traverse and explore them for enterprise transactions and mining. Temporal property graphs are a recent variant where time is a first-class entity to be queried over, and their properties and structure vary over time. These are seen in social, telecom, transit and epidemic networks. However, current graph databases and query engines have limited support for temporal relations among graph entities, no support for time-varying entities and/or do not scale on distributed resources. We address this gap by extending a linear path query model over property graphs to include intuitive temporal predicates and aggregation operators over temporal graphs. We design a distributed execution model for these temporal path queries using the interval-centric computing model, and develop a novel cost model to select an efficient execution plan from several. We perform detailed experiments of our Granite distributed query engine using both static and dynamic temporal property graphs as large as 52M vertices, 218M edges and 325M properties, and a 1600-query workload, derived from the LDBC benchmark. We often offer sub-second query latencies on a commodity cluster, which is 149x-1140x faster compared to industry-leading Neo4J shared-memory graph database and the JanusGraph / Spark distributed graph query engine. Granite also completes 100% of the queries for all graphs, compared to only 32-92% workload completion by the baseline systems. Further, our cost model selects a query plan that is within 10% of the optimal execution time in 90% of the cases. Despite the irregular nature of graph processing, we exhibit a weak-scaling efficiency >= 60% on 8 nodes and >= 40% on 16 nodes, for most query workloads.