Furnace firing. Plenty of hot water. No heat.

The water supply to a cold water pressure washer can be warmed for better cleaning results but any hotter than hand-hot water is out and you would be risking shortening the life of your washer.

Supplying the washer from a large barrel with a hot fire underneath would be a good method - with the feed hose maintaining the level and therefore stabilising the temperature.

Trading the cold water washer in for a hot water washer or even a high pressure steam cleaner would probably be the best option.

You need to make sure that the small flex line going to the water supply is not kinked than if that dont work make sure theres no trash in the cartridge

Refer to the manufacturer's recommendations for back-flushing/descaling to flush out mineral deposits and build-up in the heat exchanger. You can check to see if this is a problem by comparing the full cold water flow with full hot water flow at the faucet. If the hot water flow is significantly slower than the cold then the heat exchanger is likely clogged with deposits and will not transfer heat sufficiently. If the flow is good then the heating element(s) maybe defective.

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If you have a hot water heater there's where you turn you heat up for your water if its hot oil its on the furnace boiler

the heater is not designed to heat wter from cpold to hot. it is only designed to maintain the hot waterb temperature. your problemis that the initial water going in is probably cold. you have to run faucet until it gets hot then start the machine.

check ur anti-scold setting when shipped from factory unit is set cold install instructions always advise about adjusting to suit your comfort--remove handle and using the blue & red adjustment tabs set the heat to your desired comfort

Try draining the system and apply air pressure (min 30psi) to each faucet. Open other hot water faucets to allow pressure to vent. Next try draining and cleaning the hot water tank.

Could the boiler be clogged with lime deposits such that the flow is restricted through the heating coils?

It sounds like you may have issues with the furnace. A qualified professional can go over the system and the house to let you know if the system and unit are properly sized. The poor performance of a furnace can be a sign of carbon buildup in the furnace.
Good luck, hope this helps.
Matt

Most likely the cause is that the furnace is firing too hot. When a furnace is installed and set up, the manifold gas pressure and fan speed has to be set by the technician so that the temperature rise through the furnace is a maximum of 50 deg F (i.e. if air enters the furnace at 68 deg F it come out no hotter than 118). The target temperature rise on any gas furnace is anywhere between 30 and 50 deg F. If the furnace runs too hot, either the manifold gas pressure must be turned down or the fan speed must be turned up to keep in this range.