The deal with the city's developer, Emaar the Economic City, will result in City Cool build, own and operate two cooling stations for residential and commercial buildings in Bay La Sun Village, one of the planned districts for the new city.
The contract is worth SR650m ($174m) and will last 25 years.
City Cool is a subsidiary of the Saudi-based Al-Rajhi Group.
Earlier this month, Saudi Arabia's Huta Group was awarded a SR83m contract for the construction of two bridges in the Bay Le Sun residential community.
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