Four low activity dM(e) stars Gl 105B, Gl 643, Gl 813 and Gl 821 were observed spectroscopically in the optical and ultraviolet regions. Despite relatively long integrations, only one of the four had detectable {\it Ca II K\&H} emission, Gl 821, which had an observed flux of 9 10$^{-15}$ {\it erg cm}$^{-2}$ {\it s}$^{-1}$, giving a surface flux of only 0.8 10$^{4}$ {\it erg cm}$^{-2}$ {\it s}$^{-1}$. Similarly, the IUE observations implied very weak {\it Mg II} emission. In one of these stars, Gl 813, the {\it Mg II h\&k} surface flux was less than 0.4 10$^{4}$ {\it erg cm}$^{-2}$ {\it s}$^{-1}$, which is a factor of two less than the previous known weakest dM(e) star, Gl 105B. Using radiative transfer techniques the {\it Ca II H\&K} fluxes have been derived for a range of model atmospheres. The zero {\it H$\alpha$} flux can be produced by a range of models, this line is therefore a rather poor constraint for the lower atmosphere. On the other hand, the {\it CA II K} flux can be dramatically effected by simply varying the temperature minimum. Comparing our calculations to the observational data, we find that the {\it Ca II H\&K} surface fluxes cannot be reproduced with {\it T$_{min}$ = 3000K. However, decreasing the temperature minimum by less than 400K produces {\it Ca II H\&K} fluxes of the order of 10$^{3}$ {\it erg cm}$^{-2}$ {\it s}$^{-1}$, in very good agreement with the weakest dM(e) stars.
{\bf Key words:} stellar activity - dM(e) stars - chromospheric modelling - acoustic heating - temperature minimum