If the bathroom across the hall has a single-lever faucet (or shower valve) it's possible that the mixing cartridge has failed and is allowing cold to mix in with the hot water so that you get warmed water at the washing machine hot water source. It is also possible that the issue is at another valve in the home, but it makes sense to start with the closest bathroom and work your way to other faucets, if needed.
Here, if that bathroom across the hall has a single-lever faucet, I'd have you turn off the cold water shutoff under the sink and then test the hot water supply at the washer. If hot water is restored at the washer then you will need to replace the mixer cartridge at the bathroom faucet to fix this issue.
If this doesn't solve the issue then you can try this at the other single-lever faucets in the house. Shower mixing valves are harder to test as they can't usually be isolated, so that's why we start at the sink and kitchen faucets. If all single-lever faucets clear as OK then you may simply need to replace the shower mixing cartridge to fix the issue or at the least, eliminate it as the source of the problem.
If you have a cold and hot water pipe connected anywhere, even by hoses (such as another washing machine), this should send up a flag and you will need to isolate things as needed to test fro cross contamination.
Finally, if you turn the water back on to any of the sinks and the water leaks at the packing nut behind the valve handle then just take two pair of pliers and use one to hold the valve firmly while turning the packing nut an 1/8th turn or so with the other pair of pliers.
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