The MRTE is a two wire device using batteries to power the electronics. I had a similar situation changing a previous 3 wire device to the MRTE last week.
Connect the red wire (L) to C (terminal 2) in the MRTE and the yellow which will be the switched live to NO (terminal 1). You do not need the Neutral (blue wire) and will have to terminate it off either as I did with a Wago connector or a single terminal off a terminal strip.
Assuming the original thermostat is wired correctly: Red is permanent live which will go to "C". Yellow is switched live which will go to either NO or NC (I think NO, but it depends which position the thermostat considers "normal" - the wrong one will turn the heating on when it's hot and off when it's cold, so just swap it over). Blue is neutral, which the new thermostat doesn't need (presumably it's battery powered?), so put a choc-block terminal on it. There should be an earth wire too, though I don't see it - but the new thermostat looks to be all plastic so doesn't need this either. Put a choc-block on this too.
For "do not need" read "*must* not connect". The blue (neutral) wire would originally have been used in a mechanical stat as the return from the accelerator heater (which reduced hysteresis). No longer used in modern digital stats. If you connect it to *anything*, it will blow the fuse under one condition or another.
There are only 3 connections in the original back box which corresponds to the wiring for a Drayton RTS1, RTS2 or RTS3 device where the yellow wire is in the position for switched live from a normally open (NO) switch contact.
Possible but unlikely. The 3 contacts in the new thermostat will be three contacts to a relay inside the device and with no connections to any of the electronics within the device. With no provision for a mains neutral it indicates that the thermostat is battery operated and the output switching is isolated from the electronics.
There is a possibility with a direct short between mains live and neutral that relay contacts may have welded themselves together or there has been some arcing. The fuse probably popped fast enough to prevent any damage.
This is exactly what happened to me when the boiler installer misfitted my new room thermostat.
The spot weld on the controller relay froze in the off position.
I called the boiler installer back and he seemed to get very stressed when I took an interested in what he was doing, eventually he left without fixing it. A bit of a shame really as he did a good job otherwise. I probably went into software developer mode, we mess so much up we are less ashamed about it, I hadn't expect him to be bothered.
After he had gone I opened up the controller and flicked the welded relay apart. I then wired the thermostat up correctly. It's been working fine for 6 years.
FWIW the old style thermostats needed three wires. When off they put a small current though a big resistor to warm the thermostat slightly. This created a hysteresis effect and stopped the thermostat switching on an off too quickly.
Thanks everyone for your helpful comments and advice. New thermostat now up and running. My uneducated attempt to install it did do some damage to the timer (a Drayton Tempus 7) when the fuse blew because when I reinstated the old thermostat the boiler responded to it regardless of the settings on the timer, so I got a click and collect Drayton LP822 from Wickes yesterday and the boiler came on as soon as I'd finished configuring it. The old one had a warranty expiry date of July 2003 so it's served me well. Thanks again.
Mine is a Drayton Tempus 6, it's time of servitude isn't over yet. I suspect you could have fixed it, but on the other hand you have a smart shiny new one and I have a dull one with a cracked plastic lid.
If buying a new one I would have been tempted to look at a wifi/smart one.
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