mahirap tanggalin ang processor sa laptop just to apply thermal paste. ano brand ng laptop? some brands are notorious for heating up fast (neo, blue). the only way to manage the heat is to get a cooling pad and use the laptop in a cooler environment (i.e. aircon)
also did you use other software besides speedfan? kung isa lang ginamit mo its possible its not giving an accurate reading. try using other software like hwmonitor, realtemp, etc. its common na hindi tama ang reading ng mga software na yan. like in my case, sa current pc ko, I used several software, iba iba ang reading
like right now
hwmonitor is saying my processor temp is 50-60, speccy is saying right about the same, speedfan is not detecting the temp from any of the cores (just HDD, GPU, etc), coretemp is also not able to detect any temps (saying core0 is 0 degrees)
so yeah the readings those software give are not really that accurate