Transforming TS for better fit I'm trying to find transformation for my explanatory variable (outside temperature) to better explain heating power usage. I have data from one year here.
data <- read.table(file="data.txt", header=TRUE, sep="\t")
Power <- as.ts(data$y)
Temp <- as.ts(data$temp_MA)
dLen <- as.ts(data$dLen)

linearfit <- lm(Power~Temp)

This linear model is not that good with $R^2=0.213$. I tried linear piece-wise transformation for the temperature and it got a little better ($R^2 = 0.228$)
x <- seq(from = -19, to = 25, by = 2) #breakpoints
require(segmented)
fit <- segmented(linearfit,seg.Z= ~Temp, psi=list(Temp=x))
summary(fit)
plot.segmented(fit) 

Does anyone have an idea what other approaches I should try for my data?
Power usage:

Temperature:

Power~Temp

Update: I'm using temperature as external regressors with day length and 168h seasonality. Day length data here. seasonality was created with:
x<- ts(1:8760,freq=168,start=1)
seasonaldummy <- seasonaldummy(x)

Auto.arima give me a nice model (4,1,1). But i'm still not happy with my temperature as an regressor.
Model <- auto.arima(Power,seasonal=TRUE,max.order=20,stepwise=FALSE,xreg=cbind(Temp,dLen,seasonaldummy),allowdrift=TRUE,parallel=TRUE,num.cores=32)

 A: Are you sure the relationship between power and temperature is linear? I could figure that during the heating season, the colder it is, the more power is used for heating; but if there is a hot summer, too, then the colder it is, the less power will be used for cooling (air conditioning). Thus the slope of the regression line reverses twice within one year. 
One solution to this problem is to assume piece-wise linearity for the temperature effect on power consumption. You would create new interaction variables of the form temperature $\times$ dummy with the dummies corresponding to temperature being, say, below -20°C, then between -20°C and -10°C, between -10°C and 0°C, between 0°C and 10°C, between 10°C and 20°C, and above 20°C. That is, dummy1 corresponds to $\mathbf{1}(temp<-20)$, dummy2 corresponds to $\mathbf{1}(-20<temp \leqslant -10)$, etc. Including these interaction variables instead of the original temperature variable would allow for the piece-wise linearity. 
The break points should be selected based on subject-matter considerations like heating threshold (when the central heating kicks in, perhaps at +10°C), cooling threshold (when cooling kicks in in most places, perhaps at +25°C) etc.
