Are all highly shock sensitive chemicals highly temperature sensitive too?
Yes -- but only to a degree

I assume you are talking primarily about explosives. All explosives are sensitive to both shock and heat to some degree. They are also sensitive to friction and spark. In most jurisdictions, as part of the regulatory approval process for new explosives the initiation sensitivity to each of these stimuli is determined with standardised tests.

In general, the lower the activation energy of the decomposition reaction, the greater the sensitivity to all stimuli. However, there is no simple relationship between sensitivity to different stimuli. Comparing two explosives, one may be more sensitive to impact than the other, but less sensitive to heat; a third may be less sensitive to either heat or impact, yet very sensitive to friction.

These sensitivities are not only a function of the chemical nature of the explosive, but also its physical form, purity, and the other ingredients in a composition. For example – not surprisingly! – addition of oily or greasy ingredients, even in small amounts, tends to reduce friction sensitivity. Most famously, liquid nitroglycerine is extremely shock sensitive, but is greatly desensitised by adsorption into a porous medium.

Again, for some important crystalline primary explosives the heat sensitivity is more or less fixed, but the shock sensitivity depends on the particle size distribution.