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In Shockley diode equation Vt is the thermal voltage and equals KT/q.
In wiki article 'T' is defined as the absolute temperature of the p-n junction.As far as I Know the junction temperature is different from the ambient temperature or room Temperature.
So why T is often taken as 300k or room temperature?Wouldn't that affect the accuracy Of this equation since Vt is not exactly 26mV?
The forward voltage of a diode will drop with junction temperature, at typical currents and around room temperature, by about 2mv/K or -0.3%/°C.
At high temperatures the reverse leakage will be much higher and the forward drop will be somewhat less.
If that difference matters to you (either because you expect junction temperature to be far different from room temperature- due to self-heating or ambient variations or both- or because you need to model fine changes), don't use the approximation for Vt. It's more than adequate for many purposes, totally inadequate for others, and marginal at for others.
The mathematical model you use for a given component is a trade-off between accuracy and simplicity. For example, real diodes have an ideality factor \$\eta\$ as well as a resistive component to the behavior, both of which can be very significant. Also Is in the Shockley equation is temperature-dependent.
Where the 0.026v does matter, a lot, is in Voltage References. I think Paul Brokaw would be pleased to have his name attached to the implementations of these crucial circuits.
In the voltage references, PTAT and CTAT circuits are combined in a carefully weighted manner, to nearly cancel the temperature sensitivities.
PTAT --- proportional to absolute temperature
CTAT --- complementary to absolute temperature
