The heater is a witness, not a suspect
Weak hot water sounds like a broken heater, and it almost never is. Look at what is actually inside one: a tank, a heating element or a burner, a thermostat, a safety valve. Not one of those parts decides how much water leaves the outlet. The machine is passive — water enters at the cold inlet, gets heated, and leaves at the hot outlet at whatever rate the plumbing delivers. So a low flow can only be one of three things: too little coming in, a blockage on the way, or a blockage at the end. Heating has nothing to do with it, which is why a heater that produces beautifully hot water can still deliver it at a trickle.
That gives the most valuable test on this page, and it costs five seconds: run the cold tap, then run the hot, and compare with two fingers. Both weak means the problem is upstream of the heater — the mains, a shared strainer, a blocked aerator — and no amount of work on the machine will change it. Cold strong and hot weak means the fault is on the hot side, which narrows it to three places. Only the shower weak with the basin fine means the shower head or its hose, and the heater is not involved at all.
The second fact explains the third fault, and it is the one people misread. A mixer valve blends cold and hot, and the thermostatic kind works by balancing the pressure on both sides. If the hot side loses pressure — scale, a partly closed valve, a blocked strainer — the core drifts towards the hot side, so flow drops and the temperature starts swinging at the same time. That pair is the signature: low flow alone is a blockage somewhere, low flow plus unstable temperature is the valve. And it explains the other symptom people report separately: someone opens a tap in the kitchen and your shower goes cold, because the balance has moved again.
Three faults, three answers
Only the hot side is weak, and it has been weak from the first second is a blockage, and the first place to look is the inlet strainer: a small mesh inside the cold inlet fitting, there to catch grit and scale fragments before they reach the machine. When it clogs, it limits the whole appliance, and the symptom is exactly a weak hot flow with a perfectly healthy cold one. Shut the supply, undo the fitting, and look — a white or grey crust, or a mat of grit, is the answer. A toothbrush and a soak in vinegar clears it, and it costs nothing.
Weak hot water with a temperature that will not sit still is the mixer. The core has drifted because the two sides are no longer balanced, and the drift both restricts the flow and ruins the blend. Before you buy anything, run the hot on its own with the cold side shut off at the isolation valve: if the flow is still poor with the cold out of the circuit, the restriction is upstream of the valve rather than in it. If it improves, the valve is the fault — take the cartridge out, descale it, and replace it if the seals are perished.
Only the shower is weak is the cheapest of the three and is not the heater at all. Unscrew the head and run the hose on its own: strong from the hose means the head is scaled up, weak from the hose means the hose itself has collapsed or furred inside. Soak the head in vinegar overnight and pick the holes out with a pin. Understand why this one creeps up on people: scale blocks the holes evenly, so the shower never feels blocked — it just gradually feels softer and weaker, and people conclude the water pressure has dropped.