Depending on the age and miles of the compressor unit I would replace the whole unit as opposed to just a clutch change.

So, you didn't replace anything? You just bridged the thermal fuse?

Yes! Just bridged thermal fuse. Please use common sense and asses condition of the clutch and compressor for any other potential problems such us clutch bearing for excessive wear and coil for sings of burning. Did compressor made any noises prior to failing. Also, you may use ohmmeter to confirm issue with blown thermal fuse. Let me know if you have any other questions.

Instead of just bridging the terminals, why not solder in a new thermal fuse if that is the problem? Once the rating is determined, they are only a couple of dollars at any decent electronics store...

If someone can post better pictures of the part number on the thermal fuse, I will try to track a source down.

@Trader4 – who needs thermal fuse behind compressor clutch? Just kidding;)
Now with all seriousness:
With over 35 years, experience working with cars and electrical / electronic equipment I (I am not forcing my opinion on everyone here) felt that bypassing thermal fuse in this particular situation is acceptable risk. Here are my points:
1. I did not see thermal fuses in the AC clutches until 21st century (Possibly it just me).
2. I did not research this, but my best guess for why it is there – avoiding clutch seizure after prolonged slippage. In this case scenario, AC belt will disintegrate and potentially damage other components. Giving this potential unpleasant scenario – thermal fuse seems like a cheap insurance policy.
3. In reality, AC clutch may slip as of result of excessive wear, excessive system pressure due to improperly charged system or overheat due to inadequate ventilation (bad Auxiliary fan, etc.) and clutch bearing or compressor seizure which is rarely happens without warning sounds
4. As most of us on this forum, I pay close attention and promptly investigate any abnormal sounds and perform maintenance as required.
5. My AC system performed top notch prior to failure and after careful inspection I believe clutch circuit became open not due to the excessive heat, but internal fuse failure due to age and exposure to the environment it located.
6. The fuse used here is about half the size of common thermal fuses available at local components store (see picture). Due to limited space and difficulty to solder new fuse in the same location, I decided to cut corner and just bypass it:(
7. My original intent was to find new or used replacement coil, but two years later I have little motivation to touch it again;)

Now for those whose clutch failed and who must fix it right:
Pics below – compressor type, original fuse and size comparison between original and commonly used in US applications thermal fuses.

eBay link for the one that I believe will work here. Please do your own research before buying. Be very careful if you decide to solder it in – melted solder applied to the leads will be hot enough to blow new fuse.
http://www.ebay.com/itm/5-Pcs-ELCUT-UMI-Microtemp-Thermal-Fuse-Axial-Type-127-TF-Cutoff-187-2A-250V-/181635002957?
pt=LH_DefaultDomain_0&hash=item2a4a4a324d

I did a few more tests a few days ago. My BMW DIS indicated that I had a clutch (magnetic coupling) problem, or.,...that it was Inactive. I cut the wire (actually was already cut,...with a crimped connector,...so I just undid the crimped connector) and put 12 volts directly to the clutch,....nothing happened. I checked the clutch wire to ground resistance with my ohmmeter and got no reading.

Lastly, I tried turning the center portion of the compressor clutch assembly, and was not able to turn it. Thinking this could mean that the compressor came apart and is seized,...which perhaps in turn blew the thermal fuse,.....there was some clattering from the area of the compressor for a few seconds while it was idling in front of my garage,.....I shut it off fairly quickly to do a visual,...saw nothing,....restarted,.....no noise now,....also no A/C When I ran a quick errand.

BTW, I duplicated all the above proceedures on my Land Rover. Disconnected the compressor from its power lead,....provided 12 volts directly to the compressor and it clicked on nicely,...also was able to turn the center portion of the compressor/clutch with little effort.

Sorry. Sounds like you need new compressor. What year is your X? Engine size? Please update your signature with details.

I've just replaced my coil pack and fired up initially, all appears working but after a 20 min test drive, fuse #48 blows. I thought clutch was incorrectly gapped (too close), so put in a shim to give a 0.4mm gap but fuse has gone again.

I note my replacement didn't have this thermal fuse, is it a requirement? would it blow the circuit? thx

it appears I had frayed wiring from coil which was grounding on compressor causing the short...