These could be related, and the cure may be just a bit of mechanical TLC. If it's a while since you had it serviced, go it a good going over - oil & filter, air filter and either clean & re-gap the plugs or renew them. A dose of fuel system cleaner or a couple of tankfuls of BP ultimate or Shell V power will do it a world of good as well. On the other hand, if all your servicng is bang up to date, check the coolant temp sensor and/or the idle speed control. The latter can get a bit gummed up and ne slow to respond; carburettor cleaner is good for cleaning it.
Hope that helps
Tim