Why is the cpu fan speeds up and cpu hot after booting

you want to use proper apps not guesses when your talking about system temps.
try realtemp http://www.techpowerup.com/realtemp/ and coretemp http://www.alcpu.com/CoreTemp/ . what you think is hot may just be that cpus running temp.
if they do turn out to be hot then check the heatsync and make sure its connected properly.
if its fine check the fan can and does run at full speed, that its clean and not making any wrong noises. check your case airflow is efficient and free flowing.
if your cpu is still to warm check bios and make sure your cpu volts haven't been messed with by loading optimized defaults.
this will default your systems clock settings and voltages.
if you cant afford a 3rd party cooler then get some better paste swapping out the default paste for high quality paste can take 5 or more 'c off your temps.
if all that is done and your temps are still high then consider a new cpu cooler and fan.