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Any forward voltage of a p-n junction exhibits a negative TC.
Due to a TC of a mobility of minority carries and an intrinsic minority carrier concentration, the TC of Vbe in Silicon is about -1.5 mV/K.
From equation for collector current Ic=Is*exp(Vbe/(kT/q))
you can get equation for Vbe:
Vbe=(kT/q)*ln(Ic/Is).
If two identical transistors are biased at a collector currents of Io and n*Io, then
Delta(Vbe)=(kT/q)*ln ,
]i.e. Tc of delta(Vbe) is positive, proportinal to T.
See in more detail any book about Analog design, for example, Razavi's "Design of Analog CMOS IC", chap. 11.
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