Scaled/weighted density plot

And to do this in base (using DanM's data):

plot(density(dat$Temperature,weights=dat$Number/sum(dat$Number),na.rm=T),type='l',bty='n')

I think you can get what you want by passing a weights argument to density. Here's an example using ggplot

dat <- data.frame(Temperature = sort(runif(10)), Number = 1:10)
ggplot(dat, aes(Temperature)) + geom_density(aes(weights=Number/sum(Number)))