High temperature solder is probably the most stable method of attachment

What are some advantages of Hi Temperature Solder?

Stable – long term with proper metal surfaces
Accurate – Can be attached to very small components

What are some of the disadvantages of Hi Temperature Solder.

Does not stick to many materials
May affect solder joint alloy composition
Expensive
Soldering skill required

You can buy high-temp solder here

Much has been said about various thermocouple attachment methods and how well they work.

What are some common methods of attachment?

Kapton tape
High temperature solder
Aluminum foil – adhesive backed
Aluminum foil – adhesive backed – framed in Kapton tape
Copper foil – adhesive backed
Epoxy – air or uv cured
Temprobe(r) - reusable adjustable probe
Sticky T/C – reusable tape – adhesive backed

“How well they work” depends.

Are they easy to attach? - How long does it take to make a good connection
Are they easy to remove? – Is the thermocouple or product damaged during removal
How stable is the attachment ?- Can I get consistent results over repeated measurements
How accurate is the measurement ? – Does the attachment method interfere with the measurement
Cost – What do the attachment materials cost
Can the attachment materials be reused?�
Can the thermocouple be reused after removal?