Splitting/y'ing a thermocouple amongst 2+ inputs
Generally that's not a problem provided there is no ground issue. 

The thermocouple connection per se is perfectly fine, and I've personally done it in many different applications (such as operating a data acquisition system, recorder or indicator from the same sensor as the controller) . 

The individual Chromel / Alumel (type K) wires are not solderable with the usual flux unless they happen to be plated. They may be solderable with very active (corrosive) stainless-steel flux. You could also use a terminal block, but the block should be kept out of the way of air currents etc. The temperature is not particularly important provided the gradients are kept to a minimum (obviously proper extension leadwire must be used, and with the correct polarity). 

It's also possible to simply daisy-chain the thermocouple extension wire from one terminal block to the next. Since the limit controller is less critical as to accuracy you could put it last. The temperature at the terminal block of the first instrument will be a few degrees higher than ambient, but that does not cause an error.  

Note: there is a small chance that one device could fail in such a way as to affect the other. So this may not be a kosher approach in safety-critical system as the redundancy is not present. There is also a possible issue with break protection, which typically puts a bit of current through the thermocouple to detect a broken sensor. If one instrument is set for high and the other configured for low they may fight. The current adds when properly configured so you might need much less total resistance of connections to keep a bit of extra error from creeping in. 

One advantage to using two completely different sensors (rather than a dual thermocouple) is that the controller can do a really good job of controlling its own sensor temperature, but not so great a job of controlling the item you're really interested in, and a separate sensor can help pinpoint that kind of issue.