Interchangeability and safety are separate requirements in IEC 60061, and cap temperature rise sits firmly in the safety half. It measures how hot the cap gets in a specified test holder under specified conditions, and the result determines the T marking that appears on the lamp or its packaging.
The T value states the maximum cap temperature the lamp is designed to produce in the reference holder at rated voltage. A luminaire manufacturer uses that number to decide whether the holder and the wiring in the fitting can survive it. A lamp whose actual cap temperature exceeds its marked value is non-conforming even if every dimension is right.
Cap temperature depends strongly on how the lamp is mounted. A lamp in free air runs cooler than the same lamp in a recessed downlight, and both run cooler than a lamp in an enclosed fitting. The test is defined in a reference arrangement, and the marked value applies to that arrangement; a fitting that traps heat can exceed it, which is why luminaire standards require their own thermal testing.
When a customer reports short lamp life or a deformed holder, measure cap temperature in their fitting before blaming the lamp. If the measured value exceeds the T mark, the fitting is the problem, and no amount of gauge checking will fix it.