Engine will not rev up when hot

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My 54reg Daihatsu Terios Sport , petrol , has a mysterious engine fault . When cold the engine accelerates and runs ok but as soon as it gets hot , it will only will only struggle to approx 1000rpm. When trying to rev the engine it coughs & splutters and it smells very hot inside the car.
The Garage as yet haven't been able to pinpoint the problem . The exhaust and cat. appear to be working ok and a fault was found on the exhaust Oxygen Sensor which was replaced . Unfortunately this has not cured the problem. Initially it seemed ok but when the engine got to working temperature the rpm dropped to around 1000 as before.
Has anyone any suggestions as to what may be causing this malfunction?
Thanks

There are 2 O2/Lambda sensors.

Did the garage replace the right O2 sensor? There are 2. One on the exhaust and one inside the engine bay before the manifold. Ideally both should get replaced. Also I take it the engine isn't over heating? Worth investing in a OBD-II scanner such as a scangauge II that will show you things like engine temperature as well as scan for ECU fault codes. If the engine is struggling with power when warmed up then it's doing so to prevent further over heating. You may have issues with the thermostat. Does the radiator fan kick in?

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'12' Plate Mazda MX-5 2.0 litre NC 3.5 Venture Roadster 160BHP
'15' Plate SEAT LEON 184 FR TDI. 240BHP/500nm Torque.
Past: '53' Plate Yellow YRV Turbo Approx. 150BHP

Still can't find what's causing the problem

Thank you for your suggestions . The Garage have now changed both the 02/Lamdba sensors, checked the catalytic converters and exhaust are clear , checked the timing mechanism is working ok but nothing is affecting the problem - it runs fine when cold but once the engine is hot it will only rev up to around 1000 rpm . When trying to rev the engine at stage , it back fires through the carburettor . Any further suggestions would be appreciated.