GJ1132 is a nearby red dwarf known to host a transiting Earth-size planet. After its initial detection, we pursued an intense follow-up with the HARPS velocimeter. We now confirm the detection of GJ1132b with radial velocities only. We refined its orbital parameters and, in particular, its mass ($m_b = 1.66pm0.23 M_oplus$), density ($rho_b = 6.3pm1.3$ g.cm$^{-3}$) and eccentricity ($e_b < 0.22 $; 95%). We also detect at least one more planet in the system. GJ1132c is a super-Earth with period $P_c = 8.93pm0.01$ days and minimum mass $m_c sin i_c = 2.64pm0.44~M_oplus$. Receiving about 1.9 times more flux than Earth in our solar system, its equilibrium temperature is that of a temperate planet ($T_{eq}=230-300$ K for albedos $A=0.75-0.00$) and places GJ1132c near the inner edge of the so-called habitable zone. Despite an a priori favourable orientation for the system, $Spitzer$ observations reject most transit configurations, leaving a posterior probability $<1%$ that GJ1132c transits. GJ1132(d) is a third signal with period $P_d = 177pm5$ days attributed to either a planet candidate with minimum mass $m_d sin i_d = 8.4^{+1.7}_{-2.5}~M_oplus$ or stellar activity. (abridged)
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