Update your PASWR2 package from http://github.com/alanarnholt/PASWR2 by following the directions. First we will change the levels of month from alphabetical to their proper order.

library(PASWR2)
summary(PAMTEMP)
      tmax            tmin             precip            day       
 Min.   :-1.50   Min.   :-10.000   Min.   : 0.000   Min.   : 1.00  
 1st Qu.:11.50   1st Qu.:  4.000   1st Qu.: 0.000   1st Qu.: 8.00  
 Median :17.20   Median :  8.000   Median : 0.000   Median :16.00  
 Mean   :17.96   Mean   :  8.152   Mean   : 2.139   Mean   :15.73  
 3rd Qu.:24.00   3rd Qu.: 12.600   3rd Qu.: 1.200   3rd Qu.:23.00  
 Max.   :40.00   Max.   : 23.500   Max.   :69.200   Max.   :31.00  
                                                                   
     month           year          tmean      
 Aug    : 651   Min.   :1990   Min.   :-4.00  
 Dec    : 651   1st Qu.:1995   1st Qu.: 7.90  
 Mar    : 651   Median :2000   Median :12.50  
 Oct    : 651   Mean   :2000   Mean   :13.06  
 Jun    : 630   3rd Qu.:2005   3rd Qu.:18.20  
 Nov    : 630   Max.   :2010   Max.   :31.00  
 (Other):3683                                 
levels(PAMTEMP$month)
 [1] "Apr" "Aug" "Dec" "Feb" "Jan" "Jul" "Jun" "Mar" "May" "Nov" "Oct"
[12] "Sep"
PAMTEMP$month <- factor(PAMTEMP$month, levels = month.abb[1:12])
levels(PAMTEMP$month)
 [1] "Jan" "Feb" "Mar" "Apr" "May" "Jun" "Jul" "Aug" "Sep" "Oct" "Nov"
[12] "Dec"
library(ggplot2)
ggplot(data = PAMTEMP, aes(x = 1:dim(PAMTEMP)[1], y = tmean)) + 
  geom_line() + 
  theme_bw() +
  labs(x = "", y = "Average Temperature (Celcius)")

Now some side-by-side violin plots.

ggplot(data = PAMTEMP) + 
  geom_violin(aes(x = month, y = tmean, fill = month)) + 
  theme_bw() + 
  guides(fill = FALSE) + 
  labs(x = "", y = "Temperature (Celcius)")

ggplot(data = PAMTEMP) + 
  geom_violin(aes(x = as.factor(year), y = tmean, fill = as.factor(year))) + 
  theme_bw() + 
  guides(fill = FALSE) + 
  labs(x = "", y = "Temperature (Celcius)")