Good after sale service - In Malaysia, that mean Dell, Lenovo (if upgrade warranty), HP ....
Your current laptop overheating could be due to dust clog up in internal fan, air inlet / outlet. Clean it up, re-apply thermal paste, and see how it go.
You should do this for the new laptop you are going to buy as well (i.e. keep it dust free, otherwise the same heat up problem will happen).
As long as the laptop has HDMI port, you can connect it to HDTV to watch 1080p movies. Intel HD 4000 IGPU can handle 1080p well.
"nothing smaller than 13" " - that mean 13" is ok right?
Dell 13"
XPS13, i5-3317U + Intel HD4000 + 128GB SSD@RM3299[1.36kg], 4GB, W8, backlit
14"
Inspiron 14z, i5-3317U + AMD HD7570M + 32GB SSD + 500GB(5400rpm)@RM2449[1.87kg], 4GB, W8 *no VGA port, OD
XPS 14, i5-3317U + Nvidia GT630M + 32GB mSATA+ 500GB(5400rpm) HDD + (1600x900)@RM3749[2.1kg], 4GB, backlit, spill resistant keyboard, W8
Lenovo 13"
IdeaPad Yoga 13, i5-3317U + Intel HD4000 + 128GB SSD@RM3399, 4GB, 2 years; colors: grey/orange
14"
S400, i5-3317U + Intel HD4000 + 24GB mSATA + 500GB(5400rpm)@RM1999[1.8kg], 4GB, W7HB; AMD HD7450M/W8@RM2199
HP 13"
Envy SpectreXT 13-2106TU, i7-3517U + Intel HD4000 + 128GB SSD@RM3399[1.39kg], 4GB, W8,backlit keyboard
14"
Envy4-1111TX, i5-3317U + AMD HD7670M + [32GB mSATA + 500GB(5400rpm)]@RM2599[Beats][1.75kg], 4GB, W8
Envy [Ultrabook] (Spectre) 14-3111TU, i5-3317U + Intel HD4000 + (1600x900 Radiance) + 128GB SSD@RM3999[1.8kg], 4GB
Price is RSP, negotiable.
Use your remaining budget to upgrade / extend warranty to 3 years on site.