Here are some tutorial documentation which I found very useful at the time of learning the dlnm package. The second one in particular is extremely useful - you can find on page 5 (lines 8 to 14) the interpretation for the lag-specific risk ratios (RRs) and cumulative RRs.
In your first output, those lag-specific RRs for the first two lag indicates a modest reduction in the risk of CVD admissions in relation to temperature, those from 3 and beyond indicate a modest increase (but not significant as 95% lower bounds overlap the null value of 1). However, you should ask why does you result show a somewhat flat pattern?
Your second output - the cumulative RRs are so close to 1 with wide 95% CI having null value between them, essentially meaning that the overall relationship between CVD and temperature is not significant.
Was there a particular reason you specified your temperature effect as a linear one, i.e. " argvar=list(fun="lin")"? Usually investigators would attempt to explore the non-linear relationship in the DLNM framework by specifying a natural cubic spline (see the references provided by Anwar above). I think how you specified the postulated relationship could have influenced your results. Perhaps you can explore the non-linear relationship instead?