We report on the temperature dependence of the quasiparticle density of sta
tes in the simple binary compound MgB2 directly measured using scanning tun
neling microscope (STM). To achieve high quality tunneling conditions. a sm
all crystal of MgB2 is used as a tip in the STM experiment. The "sample" is
chosen to be a 2H-NbSe2 single crystal presenting an atomically flat surfa
ce. At low temperature the tunneling conductance spectra show a gap at the
Fermi energy followed by two well-pronounced conductance peaks on each side
. They appear at voltages V-S similar or equal to 3.8 mV and V-L similar or
equal to +/- 7.8 mV. With rising temperature both peaks disappear at the T
-C of the bulk MgB2, a behavior consistent with the model of two-gap superc
onductivity. The possibility of a particular proximity effect is also discu
ssed.