Gravity is also influenced by energy levels around it and that includes heat.
Temperature is a measure of energy density, and an energy density of any type will contribute to the stress-energy tensor, a quantity that determines the spacetime distortion. So all things being equal, a clock in a region of higher temperature, higher energy density, will run a little more slowly compared to a clock that is in a lower temperature region, and a little more slowly still compared to the minimum energy density or absolute zero.
Gravity is related to temperature in two ways, and the two of them work in opposite directions. Energy adds to gravity. Heating things just a little bit, like bringing a pot of water from 0 °C to 100 °C, the heat would contribute a very negligible amount of gravity, something in the order of 5 x 10^-3 nanograms. But the water would simultaneously expand (assuming it was liquid water to start with and not solid). This expansion would decrease its gravity. Where you see significant influences from temperature is in very hot objects such as stars.
Gravitational anomaly map of Earth
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